“I did write to The Sundays a number of times,” confides Stuart Murdoch, “That would have been quite something.” In the Crazy Horse bar, where he has just been reading extracts from his newly anthologized writings, Belle & Sebastian’s urbane frontman ponders the inevitable knockbacks faced by anyone curating their own festival. If Murdoch speaks like an old hand, that’s because he rather is, these days. Lest we forget, with 1999’s Bowlie weekender at Camber Sands, it was Belle & Sebastian who invented the left-field holiday camp takeover, setting a template for subsequent events helmed by the likes of Pavement, Matt Groening and – just a week previously – Godspeed You Black Emperor.

For all of that, it’s still faintly surreal to see the post C86 indie generation congregating around the arcades, hot dog concessions and waterslides of this unreconstructed holiday camp. This is surely what the earth would look like if the meek had inherited it but hadn’t got around to making it over. Among the line-up, some are more guessable than others. Played by Dean Wareham and his band, a set of songs by his old band Galaxie 500 is all but suffocated in a show of workmanlike competence. The Zombies get a rapturous response every time they play anything from Odessey & Oracle, though Rod Argent struggles to understand why his grisly 1972 air-puncher Hold Your Head Up fares less well. Saint Etienne beef up the beats for Only Love Can Break Your Heart and Nothing Can Stop Us and, in doing so, warm up the place for a The Go! Team performance that looks and sounds like insurrection in a kindergarten.

Other inclusions on the bill, however, are less predictable. Even if Bob The Builder and his team were doing a shift at the Builder’s Yard bearing his name, they would be comfortably drowned out by Santa Cruz’s Howlin’ Rain. Their dense riff-rock hurtles along with the improbably majestic velocity of a Sherman tank, amply illustrating why Rick Rubin is such a fan.

Over at the arena-scale Skyline Pavilion, curiosity as opposed to any outward sign of enjoyment is keeping a modest crowd before Brooklyn’s Dirty Projectors. A version of Dylan’s As I Went Out One Morning is a funk of screeching organs that unfolds over a time-signature comprehensible only to mathematicians and Frank Zappa obsessives. They’re much better doing their own Stillness Is The Move, not least because of the off-the-scale deranged vocal pyrotechnics brought to the job by Amber Coffman.

You would, at this stage, be forgiven for thinking the Bowlie throng a conservative bunch – but that wouldn’t explain why one of the weekend’s sensations turns out to be Mulatu Astatke. There can’t be more than 30 people present when the 67 year-old Ethio-jazz godfather stands behind his vibraphone and pilots his Heliocentrics along the inscrutable undulations of Yekermo Sew. The catalyzing effect of myriad tweets and texts telling friends what they’re missing means that from Astatke’s vantage point, it must all rather resemble time-lapse footage of cells multiplying in a Petri dish. Cells, at any rate, with an undeniable fancy for floral print skirts, duffle coats and DIY bobs.

Back at the Crazy Horse bar, Cynthia Plastercaster has brought a bag of her finest work to remind us that the true completist can always find an outlet beyond merely owning the records. She asks if anyone would like to come to the stage and hold Jimi Hendrix’s erect member in their hands and seems surprised when most of the take-up is from men. It’s unlikely that Julian Cope would have been invited to Butlins on the basis of anything he has recorded in the last decade, and his set reflects that. The captain’s hat, Ray-Bans and Neu! t-shirt don’t quite erase his unlikely resemblance to a countercultural Gillian McKeith – but that’s mercifully forgotten when he sits at the Mellotron to deliver a time-stoppingly beautiful version of The Great Dominions. Directly afterwards, he gazes down at a setlist which also takes in Upwards At 45 Degrees, Head Hang Low and Double Vegetation – and rightly surmises that “the songs I see there are classics.”

The resurgent Edwyn Collins would have reasonable cause to make the same claim. Teenage Fanclub have stuck around an extra day after their Friday set to act as his backing band. Norman Blake is a picture of wish-fulfilment singing blithely along to What Presence and sharing vocals on Falling And Laughing. A mere rehash of old Orange Juice glories would have been fine, but the extraordinary thing about Collins’ set here – irrespective of his 2005 stroke and its subsequent effects – is that nostalgia has no place in several of its finest moments. Complete with a vocal turn from Ryan Jarman, a high-voltage canter through What Is My Role, from current album Losing Sleep, eclipses even a Franz Ferdinand-assisted A Girl Like You.

The proliferation of Scottish indie alumni spanning several eras – Franz in their own right (covering The Sonics’ The Witch!), Sons & Daughters, The Vaselines, Camera Obscura and an hour of exquisite lysergic freak-folk from Trembling Bells – means that, at any time, you never quite forget whose festival you’re attending. To watch Isobel Campbell alongside Mark Lanegan dispense a hangover-soothing afternoon set is to boggle that she was ever in Belle & Sebastian. Lanegan – ever the unlikely muse in this alliance – sings the back-porch lullabies written for him by Campbell with the focus of a schooled actor. Elsewhere, Belle & Sebastian guitarist Stevie Jackson gingerly reveals his light from the bushel where it resides and reels off a series of startlingly good originals: among them a piece of Nilssonesque whimsy called Where Do All The Good Girls Go and a Jonathan Richman-like thing called Press Send, which ponders the agony of declaring your feelings for a girl via email.

No musician has ever looked more like a Julian Opie painting than Jackson, who avoids performing any of his band’s songs “because they remind me of work”. It’s almost certainly a joke, although it has to be said that there are moments during his “proper” group’s headlining set that rather come across that way. Ironically, given their early reputation for shambolic live performances, the problem might be just how well-drilled the the 21st Century Belle & Sebastian sound – a point somehow brought into relief when Murdoch momentarily goes off-piste during Step Into My Office, changing “burned out after Thatcher” to “burned out… actually by the present administration… I’m sick of it!”

Being Belle & Sebastian in 2010 means that the venues you play are bigger than ever, but the songs that still go down best of all are the ones that date back to an era of church-hall rehearsals and home-made Super 8 videos. A clangorous Lazy Line Painter Jane still floors you for its ability to find common ground between the worlds of Bill Forsyth and The Velvet Underground. Massed clapping greets a vertiginious sprint through Sleep The Clock Around, which ends with Murdoch handing out Jim’ll Fix It badges to a hand-picked coterie of on-stage dancers. An avowed fanboy like Stuart Murdoch is savvy enough to know that Belle & Sebastian will forever be important to a generation of fans for whom they came at precisely the right time. Why shouldn’t anorak-attired indie loyalists have a Grateful Dead of their own? And why shouldn’t that gathering post be Belle & Sebastian? No reason. No reason at all. But it remains to be seen if that’s ultimately all that Belle & Sebastian wish to be.

Having been singled out by Stuart Murdoch, the dozen or so fans dancing at the back of the stalls commence what must be the politest stage invasion in history. Even when invited up there by the singer of the band they’ve come to see, they huddle together, stage right, excited but respectful of Belle And Sebastian’s personal space. It’s a fitting way to behave around the Glaswegian octet, whose 1996 breakthrough album If You’re Feeling Sinister reminded many of us that, before Oasis and their chums hijacked it, indie music used to be made for and by people who wore anoraks and didn’t think it weird to go to libraries. After seven years laid low with M.E., this outpouring of one man’s own interior world singled out Stuart Murdoch as one of the best songwriters of his generation. All things considered, it’s no surprise that this was the one they chose when asked to perform one of their albums as part of this autumn’s London-wide Don’t Look Back season.

For those of us who remember the live performances which accompanied If You’re Feeling Sinister on its release, it’s odd to hear these songs delivered with a degree of professionalism. Even when “warming up” with a selection of lesser-known songs, they no longer play like a school orchestra conducted by the only Smiths fan in the staff room. Indeed, thanks to a new string section, the plight of Fox In The Snow’s metaphorical protagonist addresses the throng in new baroque colours. Seeing Other People rolls along like the opening credits to an unmade Bill Forsyth film. The singer’s demeanour lies in contrast to the former church janitor who once seemed to regard his audience with a mixture of suspicion and fear.

Tonight, he approvingly notes the quantity of bicycles chained outside The Barbican and relates a dream he had last week about ex-girlfriend and former multi-instrumentalist Isobel Campbell: “She said, ‘I’ll do the gig if you keep a taxi running outside.’” A moment of reverie ensues when he absently adds, “I do miss her.” Then his band launch into Get Me Away From Here I’m Dying – the song which, more than any, underscores the young Murdoch’s audacious facility with a lyric. You don’t pen lines like “Nobody writes them like they used to/So it may as well be me” without some notion that you have the songs to back it up. How touching also, that far from treating it like an albatross, the enormity of what they achieved with this album means as much to Belle And Sebastian as it does to their fans.

It was probably something to do with the 3D glasses – handed out in cute litte Autobahn envelopes – that made people assume that cinema conventions would apply. In other words, there was little rushing to the front. Instead, Kraftwerk fans found a likely spot on which to place their cushions (yes, they were handed out too) and waited. But as it turns out, from the barrier, it all worked just as well. An enormous impassive robot lurched out from the screen, seemingly so close to Ralf Hütter, that it took a feat of immense communal restraint not to shout, “BEHIND YOU!” From thereon in, the cushions weren’t needed. A mostly standing audience of mostly men, mostly with no hair, mostly nodding appreciatively, must have looked, from the vast roof of the Turbine Hall, mostly like a gently vibrating plate of beans on toast. This first of eight shows – each devoted to one album in “The Catalogue” – started with Autobahn. It wasn’t the first album to appear under the Kraftwerk imprint, of course, but it was the first in which Kraftwerk marked out their conceptual territory – territory which 38 years after the release of that record – still informs everything they do. This marking out of conceptual territory also explains the switchboard-melting, website-crashing response that greeted the announcement of these shows. It’s just Hütter left from the “classic” lineup now – dressed in customary, grid-lined body-suit (a Tron-sie, if you will) – but the clamour for tickets suggests there’s some truth in his assertion that he and his colleagues are “music workers” (the word “robot” comes from the Czech word for “worker”) servicing the brand.

I say “some truth” because, well… you do rather pine for the immediately recognisable profile of Hütter’s departed foil Florian Schneider silhouetted against the graphics that constantly shift behind the group at their light-framed work pods. A couple of months ago, another mainstay of the classic lineup Karl Bartos drily pointed out that he’ll be represented at the shows by the melodies that he wrote for The Robots and Computer Love. For all of the rhetoric about anonymous “music workers” though, the thing that made this feel like a Kraftwerk show was the immediately recognisable voice of Ralf Hütter – palpably the same slightly nasal timbre that drily referenced The Beach Boys’ Fun Fun Fun when he sang “Wir fahr’n fahr’n fahr’n/Auf der autobahn.” It was the same Ralf Hütter at the Turbine Hall who sang into his mouthpiece, eyes closed with something disconcertingly close to emotion, as he played the extended arpeggiating coda of Kraftwerk’s most iconic song.

In a micro-world set out as deliberately as this one, certain details were inescapably curious. There had always been a backward-glancing element to Kraftwerk’s futurism: the affection for constructivist fonts; the white-faced, red-lipped Man-Machine look that consciously harked back to the silent movie era; the hand-tinted, overly-posed, photoshoots used on the Trans-Europe Express sleeve. And here at The Tate, some of those elements persisted. The autobahn was almost deserted; the cars were classic German emblems of post-war optimism: an old Mercedes, an original Beetles and a VW camper. A graphic of notes emerging from an old car radio was so simple that, you half-expected the Grange Hill opening credits sausage to suddenly hove into view.

But if the visuals were a quaint throwback, it was equally clear that all the technological stops had been pulled out to push the sound into the realms of perfection. And it really was that good. Bass that seemed to enter upwards through your spine from deep beneath the ground merged with Hütter’s treacly vocoderised tones. As a globe wreathed by a revolving Kling Klang imprint hanged suspended behind Hütter and his co-workers, Henning Schmitz, Fritz Hilpert and Falk Grieffenhagen, Kometenmelodie 2 completed its ascent through the octaves to a chorus of cheers. No less affecting was the modulation from night to day represented by the shift from Mitternacht to Morgenspazierengang, complete with a rising chorus of oscillations that appeared to mimic birdsong.

If you were lucky enough to get tickets for one of these shows, but not lucky enough to secure tickets for your preferred Kraftwerk album, the good news is that you might yet hear a sizeable chunk of your first choice. Best represented of all was The Man-Machine. Unlike Spacelab – a punchy and propulsive revision of its recorded counterpart – other songs from the album stuck close to their original versions. For the visuals, quaint literalism prevailed once again. For Neon Lights, luminous signs – “Hotel Cristalli”; “nachtcafe” – appeared to float serenely around the group – accentuating this most celestial of love letters to the city at night. For The Model, Hütter looked up to face the audience for the first time as footage familiar to anyone who had seen shows over the previous decade – black and white images of screen stars from a bygone age – played out once again. If the visuals seemed to be extolling a brand of futurism had long become obsolete, the effect was compounded if you turned around to face the audience. The 3D glasses sitting on everyone’s noses weren’t the plastic ones favoured in modern cinemas. These were the old-fashioned classic cardboard-framed sort. From the group’s vantage point, it must have looked like one of those old photographs depicting cinema audiences in the 1950s stereoscopic cinema boom.

These days with Hütter, it all seems to be about “Mimimum – Maximum” approach – the process of achieving the maximum response by producing the most minimal art. In a live context, sometimes you felt that worked; other times less so. In 2013, the “Minimum – Maximum” approach has no time for anything that might seem like the merest concession to showbiz. Hence this time, there was no Pocket Calculator, the Computer World song which, as recently as 1991, would see all four members of Kraftwerk emerging from their work stations to play on their hand-held pocket calculators, even handing them over for fans in the front row to “play a little melody.” With both percussionists from the “classic” line-up long gone, the only physical exertion visible from the floor was represented by monochrome footage of cyclists negotiating mountain terrain on Tour de France. No sign, either, of the robot doppelgangers to whom Kraftwerk delegated one or two songs on The Mix tour. Boo. Elsewhere though, the “Minimum-Maximum” method yielded spectacular results. Train tracks, represented merely by white lines on black, snaked hypnotically around the screen as sleek, minimally rendered trains whizzed out of the backdrop with an efficiency that – certainly compared to deregulated chaos of British railways – assumed an unattainable beauty.

At moments like these, you were reminded why – despite having innovated themselves into paralysis – the prospect of new Kraftwerk shows inspired such a feverish response. So much of the music they chose to play tonight previewed the way we live now. It’s a point, of course, that gets made almost every time someone sets about deconstructing the appeal of this music. But there’s still something incredibly powerful about watching Ralf Hütter – now 66 – hymning a world in which people can order their love lives with the help of a computer. Lest we forget when Computer Love was released, IBM had yet to even launch the PC. Back in 1976, Radio-Activity brought a similar prescience to bear upon Kraftwerk’s music: portended the supremacy of wireless communication. It’s perhaps a shame that, post-1991, that the same song has had its horizons narrowed with the section that lists nuclear power’s rollcall of infamy (“Chernobyl, Harrisburg, Sellafield, Hiroshima”). For all of that, the 2013 live version was truly breathtaking, billowing out demonically from a tough, terrifying acceleration of a beats, into a sinister fug which more closely mirrored the song’s original arrangement and, finally, stepping up the beats to an outright funk.

If Hütter had been at all burdened by the weight of expectation, it only showed at the very end, when he let forth something like a smile of relief for Boing Boom Tschak. One by one, during Music Non Stop, his co-workers departed their stations and bowed. As they did so, Hütter could be seen doing something dangerously close to a dance. When it was his turn to take a bow, he did so with a “Goodnight. Auf Wiedersehen. See you tomorrow.” After an evening in Kraftwerk’s world, the lights went up, we left and realised that, actually, we were still in Kraftwerk’s world. That, as much as anything we saw in during the previous two hours, was the measure of their achievement.

“We’ve only been away for 12 years – you can make more noise than that!” exclaimed drummer Carl Palmer towards the end of this 40th anniversary reunion from the proggiest of all the 70s prog-rock vanguard. In fairness, an audience that had thinned out considerably towards the end of this year’s rock-centric High Voltage Festival lacked the numbers to make much more noise.

Even when the group first aired Tarkus, twenty-minute suites which depict destructive armadillo-like automatons that hatch from eggs inside volcanoes were an acquired taste. However, those who weathered the humidity to hear the song which also doubled up as the title of the group’s second album, knew what awaited them. The face may be creased and the hair suspiciously lustrous, but Keith Emerson has still maintained his peculiar habit of miming along to his own intricate soloing. He and Palmer set about a prolonged duel which, you suspect, symbolized the battle between Tarkus and his manticore avenger. If you shut your eyes, it must have been like boarding a rock Tardis bound straight for 1971. If you opened them again and fixed your gaze on the astoundingly shoddy on-screen graphics – pictures of various ELP albums moving around – the same applied.

With so much showboating going on around him, Greg Lake carried himself with the air of a man relieved of the pressure to do the same. For two of the group’s prettiest songs, Lucky Man and From The Beginning – both sole Lake compositions – the amply upholstered singer swapped his bass for an acoustic guitar. The resulting performances served reminder that, for those determined to find it, instances of restraint and economy can be found in ELP’s oeuvre.

For all of that, however, remembering ELP’s oft-overlooked facility for understatement wasn’t foremost in the thoughts of anyone who had made it this far. A huge cheer greeted the group’s adaptation of Modest Mussorgsky’s Pictures At An Exhibition – possibly the only time the word Modest will ever be used in conjunction with Emerson’s keyboard playing. After a brief pause for fireworks, their biggest hit – the trio’s discofied reimagining of Fanfare For The Common Man – was no less compelling for its inevitability. As the dismantling of the nearby carousels and rides began in earnest – if you like, a fun-fair for the common man – a précis of the final ten minutes read like a tick-list of everything that had set ELP apart from their peers in the first place. A solo from Palmer which incorporated more nudity than was strictly necessary, although some prolonged upside down keyboard showmanship from Emerson offered a useful diversion.

A fountain of sparks signalled the end of the show – although that wasn’t strictly necessary. The bit where Emerson wedged the kitchen knives into his keyboard and then pushed the whole thing onto its side suggested that, for now, the trio’s work here was done.