Radiohead’s ability to continually impress is considerable. Most common or garden international rock phenomena will manage to create one moment of truly inspired musical magic in their time: Nirvana, Travis, Alanis Morissette. The really lucky ones might even manage a couple: Oasis, Coldplay, Red Hot Chili Peppers. Radiohead have managed three. With the release of In Rainbows late last year, they added a third bona fide classic to their armoury alongside The Bends and OK Computer. Only REM can claim such levels of contemporary commercial and critical success.

With In Rainbows, Radiohead learned all about the art of judicial editing after the laborious and frankly turgid affair that was 2004’s Hail to the Thief and left off the extraneous stuff, saving it for the special edition of the album. The stripped-down album was likened in its reviews to Lou Reed’s Transformer, David Bowie’s Hunky Dory and The Beatles’ Revolver. A concise, deliberate and wholly focused statement of intent, this is Radiohead minus the navel gazing, a streamlined, dynamic, thrusting rock beast, distilling ideas down into vibrating chunks of energy.

The band has had to overcome urges in the past to ‘be’ Radiohead and fulfil some assumed role as a stadium rock band. Such converse thinking gave birth to 2000 album Kid A as Radiohead sought to redefine their role after the global success of OK Computer. Drummer Phil Selway admits there is a temptation to lose focus.

‘There’s a danger of trying to second guess where this concept of Radiohead should go, and not actually getting to listen to what’s happening between the five people in the room.

‘The whole process of making music is very self-indulgent anyway, spending all that time thinking about the music and yourself and then you talk about yourself an awful lot and you go out and do the shows and you are the centre of that universe. It can be very unhealthy. You have to find ways of pricking that bubble, just to remind yourselves that what you’re actually doing here is creating music. That’s significant as it is, and that’s as it should be.’

So much of maintaining status at the top of the heap in rock music is about control and maintaining that control, but few major rock bands have been so free with their approach to their work as Radiohead have in recent years. They, wherever possible, have handed responsibility over to the listener, be it a remix, a video or choosing just how much to pay for their album.

‘I think for quite a while now we’ve had a lot of music pre-packaged and handed down to us in a very particular way,’ says Selway. ‘As a band there have been expectations that you’re presented in a particular way as well, which can become a bit staid, so I would hope that this more direct connection we’ve made is a positive thing.’

Singer Thom Yorke has managed to successfully get the backs up of sundry multinational corporations and governments in his very public championing of certain social causes, in particular, Friends of the Earth. He, for the most part, comes across as a layman with genuine concerns, using a platform for all the right reasons.

Selway reckons the band’s, and in particular Yorke’s, synergy of music and politics works well. ‘Thom presents his views in a very good way I think, although it’s more an extension of the music than the premise for making it. He manages to tread a very fine line, as it’s a difficult one to get right, and he does it well. In the short term, it’s a very good way of drawing the spotlight to issues that are part of a bigger picture such as bringing an organisation like Friends of the Earth, and all the different things that they do, to people’s attention. It can work very well in that context.’

Radiohead, as a group, have even attempted to address their own collective carbon footprint, given the massive energy and pollution costs incurred in taking a huge production like theirs around the world. They’ve also urged their fans to consider how they travel, advocating car sharing and public transport to get to their shows.

Such concerns are all symptomatic of the way the band has developed in recent years. While comparisons have been made in the past between Radiohead and Pink Floyd, the innovations Floyd made in the 1970s were solely about their ‘art’, refining the scale, scope and design of their albums, concerts and films. Radiohead’s innovations have been in their engagement with the outside world; in politics, both personal and party, and technology (the Scotch Mist webcast showcasing their album live at the turn of the year), fan remixes of single ‘Nude’ and fielding entries for an animated video competition for songs from In Rainbows. All of which makes the clichéd notion of the rock dinosaur seems very distant from this particular band of millionaires.

Radiohead have been been accused of being miserable bastards on plenty of occasions. Angst is something they’ve successfully traded in for many years, and be it the teen no-one-understands-me angst of ‘Creep’, the more adult toying-with-my-own-mortality angst of ‘Airbag’ or the ecologically aware everything’s-bloody-melting-global-warming angst of ‘Idioteque’, they have managed to make displeasure very much their business.

The chirpy, self-effacing, optimistic, really quite bashful character on the phone from his (presumably) palatial pile in Oxfordshire doesn’t quite fit with the glum persona. Is there a chance he and his band mates have been misrepresented by the press all these years?

‘No, I don’t think there have been misconceptions about us really. The [miserable reputation] is a fair cop,’ admits Selway. ‘One of the big causes of that was Meeting People is Easy [the 1998 documentary showing the band being downright glum on the OK Computer tour] and that was only ever kind of one part of that year. It was a very dominant part of the year but it did have its lighter moments as well. We have always been quite a serious band and hopefully we’re a bit more playful now; I think we’re getting there.’

Ultimately, there’s little at stake for Radiohead. Thom Yorke could stop tomorrow, go buy a hill somewhere in Wales, sit on top of it pondering the end of the world, and he’d still have a breathtaking musical legacy. While they’ve had their fair share of jack-it-all-in moments, not least during the making of In Rainbows, Selway is adamant there is still ample reason for them to continue.

‘Every record we’ve done has had its fair share of those moments. Especially at times when you don’t actually have much to show for the work you’ve put in. Then inevitably you do question whether you will have that kind of vitality about what you’re doing and whether there’s still that chemistry between the five of you but, having put 22 years of work into the band now, we’re not prepared to throw it away lightly. That probably gets us through the rather more lean periods.’

Radiohead play Glasgow Green, Fri 27 Jun.