Jonny Greenwood: Lights, camera...indie superhero action!

Jonny Greenwood shuffles into view, grey Converse trainers squeaking against the floor.

A rock star, in the traditional hell-raising sense, he is not. Rather, as a member of one of the most cultured British bands of the past two decades, who turns 40 at the end of the year, he is shy, softly spoken and mildly ill at ease. According to one of the myriad Radiohead fan sites, he doesn't enjoy interviews "because he feels he comes across as an idiot". He doesn't, by the way. But his body language on stage – head down, fringe furiously flapping as he grinds into his guitar – does suggest he prefers to leave the showmanship to lead singer Thom Yorke.

I'm reminded of the time he said, in the wake of the success of the band's third album, OK Computer, "It feels like Radiohead are famous, but that no one knows who we are. Which is brilliant, really." So today must be a difficult day. Here he is, without his bass guitar-playing elder brother Colin by his side or any other Radiohead member, for that matter. As close as he may ever come to being a frontman, he's readying himself to talk about his new score for the film Norwegian Wood, an adaptation of the Haruki Murakami novel by the Vietnamese director Anh Hung Tran.

It's his second feature film composition, following his superlative work on Paul Thomas Anderson's 2007 oil baron drama There Will Be Blood, which earned him an Ivor Novello award and Bafta and Grammy nominations. Whereas that was thunderous and unsettling, an "atonal drone masterpiece", according to one critic, Norwegian Wood is delicate, melodic and playful, chiming perfectly with this late-1960s-set love triangle about a trio of Tokyo students. (It's performed by the BBC Concert Orchestra and the Emperor Quartet.)

Though the two didn't meet until 2008, Tran and Greenwood's paths have crossed before: the director previously used Radiohead's breakthrough track "Creep" in his 1995 film Cyclo (the same year Greenwood married Israeli-born visual artist Sharona Katan, with whom he now has three children). "He had quite strange instructions and descriptions of how to write the music," says Greenwood of his director. "We'd watch the film together, and he'd pause the film at a certain point and say 'Look at [that character's] face here. Write some music about that expression.'"

Greenwood even turned soundtrack supervisor, suggesting Tran use German group Can (one of the earliest "Krautrock" bands, whose "slightly aggressive, slightly dark and youthful" sound remains one of Radiohead's major influences). Then there was the question of The Beatles' song referenced in the title (and beloved of one of the film's characters). "I recorded a version of it on the guitar," says Greenwood. "There was talk that they might not get the permission, so they'd need a version of 'Norwegian Wood'." In the end, it wasn't needed, much to his relief. "It's not very good," he whispers.

Greenwood has been working independently of Radiohead for a while. Back in 2004, a year after he provided the music for the documentary Bodysong, he was hired as a composer in residence for the BBC Concert Orchestra. The association continued across his soundtrack work and into lush experimentation, culminating with a one-off performance in London's Queen Elizabeth Hall last October of his 2004 composition Smear (effectively a showcase for the organ-cum-theremin hybrid, the ondes Martenot, one of the odder instruments Greenwood has mastered over the years).

Greenwood has just signed on to score Lynne Ramsay's new film, the adaptation of Lionel Shriver's novel We Need to Talk About Kevin. But he is quick to contrast his approach – "long, long days, with no interruptions" – with what he calls "real soundtrack writers [who] have a deadline": "And that's not as much fun as having lots of time and writing too much music and there not being a panic. I'm happy to write 10 times too much music," he says, noting that both Anderson and Tran used about a quarter of what he produced. What he refuses to do is label a soundtrack as his attempt at a "solo album", "because it's so wrapped up in the film, which is where I'm happy to be". He looks down for a second. "Which is why I'm happy with Radiohead and then this. It's not exactly hiding behind something ... but it is, a little bit."

Inevitably, though, the conversation turns to Radiohead's new album, their first since 2007's In Rainbows shocked the music industry when fans were invited to choose their own download price. It should be pointed out that our conversation takes place well before the rushed release last month of The King of Limbs. "There are more than 10 [songs]," he answers. "To me, it sounds like they're all 99 per cent finished. But my quality level is a little bit lower than everybody else's. I'm impatient, childish. But the others are like, 'No, this is nearly right. Let's get this right.' And looking at our old albums, they've been right in the past. They're probably right now."

Announced on a Monday, due on the following Saturday, pulled forward to the Friday – the arrival of the band's eighth studio LP caught everyone by surprise. In the end, there weren't "more than 10" songs – just eight – fuelling internet chat that a follow-up is fast approaching. Though when is anyone's guess; since the download-it-for-£6 release, every band member has remained tight-lipped (including Greenwood, who declined to answer any follow-up questions about The King of Limbs for this feature).

Back when we spoke, I ask if he thought the pay-what-you-like release of In Rainbows was a risk. He nods. "We were curious to see what people would ask themselves at that moment where they go 'What am I going to pay for this? What's it worth? What value does music have?' And everyone – if only for a few seconds – must've had that thought. A lot of people would give justifications as well. You'd get messages saying 'I gave three quid, which is all I can afford but I think it's fair to give you something.' That was weird." And perhaps not worth repeating. Though In Rainbows was a commercial and critical success, most customers opted to pay nothing for the digital download.

Whatever the rationale behind Radiohead's release schedule – a cheap digital download will be followed by CD and vinyl versions – Greenwood is clear where the future lies. "I've seen 13, 14-year-olds opening CDs as though they're records from the 1920s, going 'Look at this – there's a little book!' ... That makes me think the format has probably had its day," he says. "Every American college student goes to college with a hard drive. They take their laptop. There's not a CD player in sight."

'Norwegian Wood' opens on Friday