Singer Thom Yorke's political pronouncements against globalisation, the Iraq war and Tony Blair (he recently refused to meet the latter, as the thought made him "physically sick") have meanwhile made him a cultural figurehead beyond his music; but it's a status this basically shy man seems uncomfortable pursuing.
So while Radiohead in 2006 remain Britain's most revered group, their future seems starkly uncertain. They no longer even have a record label. The UK tour of relatively small halls which starts tonight is, then, both the first chance to hear new songs from their crucial, upcoming eighth album, and to judge whether they remain vital pioneers.
They walk on without ceremony. Aggression and urgency seems ratcheted up at once. For "2+2=5", Yorke's trademark agonised falsetto blasts to the back of the hall. The first new song, "Bangers and Mash", concerns the bands bolshy mood. Tumbled down garage rock that seems ready to surlily expire in an adolescent spasm of feedback inside a minute, grand, ambitious structures can still be glimpsed at its base.
But when old favourite "Lucky", Radiohead instead emerge as a band at last willing to embrace their contradictions. Begun semi-acoustically it is a song of pulsing anxiousness. Describing a man whose luck is bound to be snatched away. But when the lights flash up as it surges into its chorus, and Yorke's great voice keeps a balance between sneering and yearning, a defiant, stadium-sized hope emerges anyway. The next step down this road would be the docile palliatives of Radiohead's unwanted offspring, Coldplay. But Yorke is too genuinely troubled to let that happen.
The new "bodysnatchers" then tears up the place again. The insolent yet fragile defiance of authority which has characterised their recent records emerges again, as Yorke spits: "I don't understand a word you say," as if to some nameless Blairite. The strutting confidence of the music, with Jonny Greenwood's guitar playing a sort of sophisticated punk, drives the mood home. Then when angst-meister Yorke starts a silly little dance to a calypso number it's hard to know what to think. Yorke then makes a solo, folk-style start to several OK Computer songs. The crowd claps along, but he quietens until they stop. Stadium impulses, encouraged a moment ago, are now carefully defused. Still, ghost-sythed choirs and another anthemic ascent eventually give the crowd what they want.
"The next song has been kicking around a long while," Yorke says of another, unidentified new one. "As," he concedes, "have we." Lilting, mellow and understated, it sounds, encouragingly, not like Radiohead at all. When the familiar, ferocious hit "Paranoid Android" follows, it's quite a disappointment.
The first, swift encore reinforces this feeling, when Yorke sings "There There" in a style of sustained but by now over-familiar passion; Radiohead by rote.
Then, in a gig which appears to deliberately seesaw between old favourites and fresh adventure, Kid A's "the National Anthem" earns its place in 2006.
Radiohead have made peace with their past tonight. But perhaps they should just let it go. Its the odd, diverse song they are writing now which sound like a band with a future.