What do people most often get wrong about Radiohead?

Thom Yorke: We play up to the tortuous thing a bit too much. It's not quite like that in the band. But also, this idea that there's some sort of masterplan, that we've got some sort of clue what we're doing... We haven't.

Ed O'Brien: I used to think that maybe people didn't know that there's actually a great sense of humour in the band. But maybe the webcasts and a few of the things we did last year show that we're not entirely super-serious all the time. You can't do what we do without humour. It's a lot easier to be melancholic in music. We struggle with songs of joy. That's the tough part.

Phil Selway: People have got a pretty accurate take on us, I think. It can be uncomfortable because some of those takes are less than flattering, but they're probably valid. You know, po-faced and over-serious... fair point, really. People are starting to pick up on the more playful side of Radiohead, which we hope has come to the fore in the past few years but, you know, no smoke without fire.

Jonny Greenwood: That we're grumpy. People confuse the work with the people who make it. We're not necessarily like our songs. Also I think they misunderstand Thom, and how really tiresomely energetic and enthusiastic he can be. Even when the rest of us are flagging, he's the one with the energy and the excitement who's saying, "Come on, this sounds amazing, what you're doing is great." That's really good for us and I don't think anyone knows it.

Ed O'Brien is a happy man this Thursday lunchtime. Not only did Radiohead play two fairly flawless shows for the BBC yesterday but his beloved Manchester United beat Roma 2-0 in the Champions League at the Stadio Olimpico. "The football was better than the gig," he beams. Being Oxford-born and now resident in north London, Ed clearly fits the description of the Man U fan to a tee but at least he went to Manchester University. He still knows "a few boys" at Old Trafford who get him tickets, and is concerned that Mani of The Stone Roses/Primal Scream has defected to the breakaway anti-Glazer team AFC Manchester. Famously the Tall One (six feet five), Ed is fantastic company, interesting, funny and thoughtful. He's also comically restrained - the strongest word he can find to condemn U2's How To Dismantle An Atomic Bomb and X&Y by Coldplay (the decaffeinated Radiohead) is "pants". Ed O'Brien has a healthy scepticism of what people say about his band and an uncommon insight into its music.

"I think a lot of what drives Radiohead's music is a longing to be in the place where you're not," he says, over pasta in a cafe near the Word office. "Or maybe not wanting to be where you are. We were never like the people at school who were happy-go-lucky. We're all from a very comfortable backgrounds in Radiohead but what fuelled us? Well, quite sad childhoods I think." Ed's parents split up when he was ten and he describes his own childhood as 'deeply unhappy". Radiohead's music of course has its morose aspect (though I'll discover that more than one member is burstingly proud of the scene in Father Ted where a melancholic young priest, rescued by Ted and Dougal from his own black dog, is sent spiralling back into depression when he hears Radiohead's Exit Music (For A Film) on the radio). But Ed's response to the sadness in his past seems to be to throw himself into the joys of creativity. "I'm not sad about my childhood now - I've got a great family of my own," he says. "But it's part of your journey. There's always something with musicians. Most of us have shit to deal with but we're British and we don't like to moan about it. Music can be a way to deal with it. I think our music takes you out of your place and maybe, hopefully, alleviates it." One of the few guiding principles for In Rainbows, he says, was that they wanted to capture some of the simple joy at being alive. One of the departure points, bizarrely enough, was Outkast's Hey Ya! They even got as far as trying, without success, to work with André 3000 on the record.

Ed is often described as Radiohead's second guitarist, which is both an over- and an under-statement. "I love sound," he says. "I'm not a technical guitarist. My heroes were Johnny Marr, John McGeogh, even Andy Summers. Sounds and riffs are the things that make you pick up a guitar. When we made our first record, Sean and Paul [producers Slade and Kolderie] said I was sort of like the keyboard player. I took great offence at the time but now I realise it's kind of true. I see myself as a bit of a sweeper - bit of rhythm, can play up front or in the hole. I'm not a Ronaldo or a Rooney: that's Thom and Jonny. But in my dreams I'm a Paul Scholes."

Making Radiohead records has become so tortuous, he thinks, because the band's success put them in a place where they could do literally anything they wanted -  and so could not work out what that anything was. "When a band becomes successful, sometimes there's nobody to look up to for a bit of advice," he says. It was a long wait for that final, elusive spine-tingle that tells you, finally, that what you've been working on really is good and worthwhile. He remembers listening to the new song Arpeggi eight times in a row as he drove to Radiohead's Oxford studio from London, as he does every morning. When he arrived, he marched into the studio and told Thom Yorke, "You have no idea how good these lyrics are. This song needs to be heard, because I'm being fucking moved by it and other people will too. It's what I want to hear and other people need to hear it as well."

I wonder how many other "second guitarists" do that kind of thing with their singers. "I'm big on intuition," Ed says, and laughs.

We talk about the band's politics and how they are mostly expressed outside the songs themselves. Radiohead have had what Ed describes as "a lot of very interesting discussions" since Hail To The Thief -  "really heated at times".

Different members have different views, and the idea that they're all identikit left liberals just isn't true. They disagreed over Iraq, for instance. "I think Tony Blair is a war criminal and he should have been impeached," says Ed, "so you get where I'm coming from. But while I don't want to speak for everyone else in the band, not everyone thinks that."

Does he agree that the band was in danger of turning into a statements group, an approach that never ends well for rock bands? He hopes not; one of the good things about In Rainbows is that it's emotional and warm, not didactic. "But to Thom's credit, he's the one who is the public face and has to do the political balancing act. I'd argue that we're not saying we know any better than you. We're in a band, but were still entitled to an opinion. And if people's opinion of Radiohead is formed by seeing Thom on the front of the Observer magazine Green issue, they're not digging very deeply there, are they? The fact that people want to talk to us and put us on the front of magazines is a blessing, not a problem for us."

Ed will have turned 40 by the time you read this. This used to signal admission to the elephant's graveyard of rock musicians; but now, when middle age doesn't start till you're 60, he's still part of the new and the now. Ed has decided not to mark the event - he and his wife had a big party when they got married and he's a little embarrassed at being the centre of attention. "I'm pretty happy now," he says. "I'm in a great band, I've got a great family, I've worked out a lot of my own demons and I'm ready for the next bit."

Read Part Four.