How we interact with each other, how we play together, how we talk about music – it’s all changed.”Two summers ago, Muse delivered an incendiary Glastonbury headline performance. But the band suffered a tragic end to what should have been a triumphant night, when Howard’s father died of a sudden heart attack shortly after the band stepped off the Glastonbury stage. “Making music was never about mixing with the in-crowd or trying to be a part of anything,” explains the band’s amiable bass-player, Chris Wolstenholme. “We never dreamt of adapting what we were doing in order to fit in with anyone else.”Sticking to their florid, arpeggioed guns while tight-trousered and even tighter-riffed bands like The Strokes and Franz Ferdinand redefined the musical landscape meant that Muse have never been very cool. “We looked different, got in fights and generally despised the town because we felt so different.”But, far from trying to fit in, Muse revelled in their status as outsiders.

From their Teignmouth days, they’ve always been the underdogs: “We were the kids in town that got chased around,” says Howard. “Whenever we play festivals it feels as though there are still a lot of people who don’t know who we are But it felt like we did a good job. By the end of our set, there was definitely a sense that they liked what we do It felt like we were winning people over. And that feels great.”Compared to the rapid rise of the Arctic Monkeys, Muse are the tortoises of the music industry Yet their slow-but-sure approach has paid off. “Maybe we have!”Visibly tickled by the notion, he collapses into laughter. “I don’t know – headlining Reading was just so surreal,” he says, determined not to get too philosophical. “The one thing I’ve always said,” continues Howard, “is, ‘when you headline Reading, you know you’ve made it.’” He grins “So, have we made it now?” he asks.

The night before that, they gave an equally breathtaking headlining set at Reading, which the NME later called “the gig of the millennium”. That might sound like undue hyperbole, but the fact is that, when Muse took to the stage after Arctic Monkeys, they made the Sheffield tykes look average in comparison. “We blew everyone else off stage,” says Muse’s impish drummer Dominic Howard with a victorious gleam in his tired eyes. It’ll take a lot more than a few sleepless nights and a day in a TV studio to smother the buzz of the weekend’s achievement.As star-struck youths, making their annual rock pilgrimage from the sunny, seaside town of Teignmouth to Reading’s rock mecca, the aspiring band dreamt of playing the headline slot.

It seems the adrenalin is still coursing through their veins from the night before.Just 16 hours ago, the band were delivering a flame-ridden encore as the final curtain was drawn on this year’s Reading and Leeds Festivals, in front of a 60,000-strong crowd in Leeds. From the spaceship-like control room, the excitable producer repeatedly calls for the volume to be turned up to so that he can enjoy the full ear-bleeding effect of Bellamy’s wired guitar riffs. But their breakthrough third album, 2003’s Absolution, forced critics into a rethink.Absolution was a revelation for everyone who had written off the band as the preserve of space-geeks and teen goths. With its exciting fusion of tempestuous rock and quasi-Baroque grandeur, the album proved that the pieces had finally fallen into place.

Now, with the follow-up, July’s Black Holes And Revelations, they’ve gone one better. Even more adventurous than its predecessor, album number four finds a mighty, more visceral Muse exploring new ground, and it was given a richly deserved place on the Mercury Prize shortlist.Right now, however, what Bellamy wants most is a long, hot bath. The band have spent the day recording three tracks for a new Channel 4 series – Live At Abbey Road – and the effort of delivering a hyper-animated performance to an unresponsive jungle of cables and mic stands has sapped much of the life out of the usually ebullient front man.Ensconced in the shiny, wooded cavern of Studio One, the band play multiple takes of each song just to be sure that every vocal warble and every exaggerated fret-move is captured. Bellamy has a well-documented affection for, let’s say, alternative thinking. The singer defends Icke’s less reptilian pronouncements, has a firm belief in conspiracy theories, such as September 11 being an inside job, and is a fan of the writer Zecharia Sitchin – who claims that humans are an alien/ape genetic mix Such opinions have had Bellamy labelled a sci-fi crank. But, having been a member of Muse for more than a decade, ridicule is something he’s had to get used to.
For a long time Muse were the high-school misfits of the music world.