It's a decade and a half since OK Computer catapulted Radiohead to global superstardom. They've now been one of the biggest bands in the world for so long that it's easy to forget how curious and unique their situation is: in a world where rock and pop is not much given to overestimating its audience, here is a band whose music long ago abandoned any pretentions to commerciality capable of filling out the kind of venues where Rihanna or Coldplay normally ply their trade.

Anyone requiring a reminder of the incongruity of Radiohead's position needs only to step inside the O2's arena. Jauntily yellow-jacketed stewards are flogging soft toys, emblazoned with the words VAMPIRES SUCK MY BLOOD in gothic script. In one of the O2's numerous chain restaurants, menus announce that it's Radiohead Night; quite how the dread-filled, agitated sound found on their last album, King Of Limbs, squares with bourbon-glazed baby back ribs and the Cajun spiced chicken sandwich remains open to question, but you can't blame them for trying.

Thom Yorke: 'weirdly magnetic'. Photograph: Samir Hussein

There's always the chance that fans turn up in their thousands in the dementedly optimistic belief that Radiohead are going to roll out the 1990s hits, in which case, they must go home tonight sorely disappointed, with only a version of OK Computer's Karma Police to remind them of the band's earlier, less complicated incarnation. As if to underline how far leftfield Radiohead have subsequently shifted, it's followed by the instrumental Feral, which in its live incarnation – scattered rhythms overlaid with echoing vocal loops and waves of electronic noise – is arguably the most abstruse and uncommercial piece of music you're ever likely to hear booming around an arena venue.

But the audience doesn't sound particularly disappointed at being presented with a set of material that draws most heavily on last year's King Of Limbs. "Are you lost yet?" asks Thom Yorke at one juncture, but they don't appear to be at all. In fact, they appear to be rapt: there's something arresting about the fact that hardly anyone seems to be filming proceedings on their mobile phones, which makes it a fairly remarkable event in the annals of modern-day gig-going.

You can see why people are paying attention. On a prosaic level, it's a visually spectacular show, the stage bathed in vivid colours, a dozen video screens suspended above the band, shifting and changing positions with each song. During 15 Step, they turn horizontally, forming a low ceiling of light above the musicians: it's a simple idea, but an incredibly striking effect, seeming to shrink the size of the stage, creating a weird sense of intimacy in the least intimate venue in London.

Moreover, Radiohead sound fantastic. Songs that passed in a blur on record sound tough and potent onstage, not least Bloom, transformed into an audacious clatter of percussion: adept at absorbing influences from dance music and electronica without being submerged beneath Radiohead's default rhythmic setting now seems to be a writhing take on funk syncopation. You're struck by their ability to shift their sound completely between songs – from the crushing bass-heavy riff of Myxamatosis to These Are My Twisted Words's spindly, thin, cyclical guitars to the unsettling electronic abstraction of The Gloaming.

Thom Yorke, meanwhile, is as idiosyncratic in his approach to holding a vast audience as the rest of the band. His hair scraped back into a pony tail, he appears to be following the advice of that terrible little poem about dancing as if no one is watching you: lost in his own world, there's something weirdly magnetic about him. Accepted wisdom suggests that kind of thing shouldn't work but it does. Then again, accepted wisdom suggests Radiohead shouldn't be here at all: that they should have alienated their mass audience long ago. Accepted wisdom is clearly wrong. A state of affairs it's hard not be delighted by.