What follows is musically a progression on from the albatross that is OK Computer, and from its experimental successors. It is not a return to the guitar music of The Bends. The Oxford quintet have managed to throw out the bathwater, but repeated listens to Hail To The Thief confirm the baby's still kicking and screaming.

From the start it's a fascinating record - in no small part due to the lyrics. 2+2=5 begins a long-play political statement, albeit a worrying one. Titles like 2+2=5 bear out a confusing world that makes little sense in the aftermath of the 2000 US presidential election and 9/11/01. The album's title has been widely interpreted as the band's impression of George W Bush's "win".

"You can scream and you can shout," whines Thom Yorke, indisputably the best whiner in rock, "it's too late now". He could be talking to the Democrats, or he could be telling Bush off about his famous "war on terror". "There's no way out," he mourns, and it seems that from the start he's decided to point out that Radiohead are not a religious sect with all the answers (some of their press coverage would have you believe otherwise) but are in fact a group of blokes doing their best to make music that matters to them.

As Yorke's vocals distort into guitar noise, fans of the band's rockier moments will be beaming from ear to ear. Go To Sleep, later on, even offers acoustic guitar, while the lead single There There has a glorious Greenwood/O'Brien guitars wig-out to recommend it.

Sit Down, Stand Up starts as an exercise in vocal harmonies over instrumentation that reminds us at once that we're listening to another Nigel Godrich-produced album - distorted glocks and piano. And then Phil Selway's drum roll indicates a second half to the track - which happens to be drum'n'bass. It's disconcerting.

Proving that lovely melodies are still possible in Radiohead songs, Sail To The Moon intersperses guitar and piano to wonderfully spacial effect.

Elsewhere, Backdrifts offers fans of Kid A and Amnesiac succour, brimming with pulsating undercurrents of synth and drum machine. "Evidence has been buried, all tapes have been erased," implores Yorke. "There was nothing we could do." It seems like he's decided that none of us can do anything - and that the fight against dark forces is already lost. There's more quasi-drum'n'bass later on The Gloaming, which manages to sound sinister and experimental while making little lyrical sense.

Roger Corman-like sci-fi effects get us going on Where I End And You Begin. "The sky turns grey where I am," mumbles our front man, and it's difficult not to think of self-parody at play. I Will sounds like Exit Music (From A Film) 2, even though Yorke's vocal layering and intense lyrics about the next generation still bring a tear to the eye.

We Suck Young Blood suggests vampire corporations at work on the bodies of the young, like some horrible parody of the forces at work behind Pop Idol. It's a distressing song to listen to - even musically it gives little respite - and is one moment that suggests the album is too sprawling for its own good, with Myxamatosis and Scatterbrain being others.

But throughout there are progressions on the various Radiohead musical themes of the past. Even the jazzy direction hinted at on Amnesiac is given free rein on A Punch-up At A Wedding.

By A Wolf At The Door (little arpeggiated chords, shambling drums at start giving way to a quasi-rap-rant with dark, confused lyrics, Yorke rapping about getting a "flan in the face" - make of that what you will), it's clear that Radiohead are more relevant and interesting now than they've ever been. Hail To The Thief shows lyrical intelligence, utter intellectual confusion and the possibilities of musical instruments. What's more, it gets better with each listen - just as any fine album should.

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Mercury Prize 2009 nominees