The underdog is finally having his day. It’s ten years since Biffy Clyro released their debut single 'Iname', and for much of the decade the Ayrshire trio’s none-more-passionate fanbase — attracted to the flickering, unpredictable, viscerally beautiful noise that frontman Simon Neil, bassist James Johnston and drummer Ben Johnston created — clutched them to their bosom and weathered the general indifference and occasional outright hostility of the more fashionable corners of the media. But that all changed with 2007's Puzzle, their fourth album and their major label debut. A devastatingly honest account of Neil’s grief following the death of his mother, the songs mixed skyscraping choruses with the band’s trademark skewed time signatures and skittish riffs, and turned them into bona fide stars.

They return this month with Only Revelations, their fifth long player that, in typical fashion, confounds expectations by sounding nothing like any of their previous output while remaining undeniably Biffyish. After the darkness of its predecessor, it’s a sparkling, peacock-bright explosion of stadium-sized rock with an underlying strangeness that oozes positivity.

"We like to try and surprise people", says Ben as the three settle back into the bar of their Soho hotel. "The last thing we want to do is make something that anyone would expect us to make. We don’t want to go for the safe bet, it’s boring."

"Your tastes grow and change, you’ve got to be honest with yourself", adds Simon. "If we were still trying to write songs like we did when we were 18 then I think we’d look and sound a bit stupid. I think it’s a more uplifting record than Puzzle. Mentally coming out of the three-year cycle that was Puzzle and the couple of years before it, we became adults to a certain extent. There’s a lot of hope and love in there."

"What boogie woogie jam?" Biffy on Jools

Only Revolutions takes it title from a 2006 novel by American author Mark Z Danielewski. It’s twisting, poetic portrait of two sides of a relationship struck a chord with Simon Neil, who got married last year.

"The book’s a love story, and it’s written in a really bizarre way", he explains. "You read eight pages of Sam’s story and then you go to the back and read eight pages of Hailey’s story. It’s only really when you read both parts that it really starts to paint a picture in your mind. It’s about two people telling both sides of the same story, which is kind of what the lyrics became on this record."

Musically, too, the band have been casting their net further than the scene that spawned them. Having had a taste of the lushness a string section can bring to their jarring art rock on Puzzle, they upped the ante again this time around, bringing in composer David Campbell to sprinkle orchestral magic across the new songs.

"I think we kind of try and twist things in our minds to think ‘what shouldn’t we do? What would the bands we love not do? Put a brass section on it’", says Simon. “And plus we wanted to make a rock record that no other rock band would make, almost a rock record that at times seems to unrock it’s unbelievable, but it’s still underpinned by a rock band."

The result is so enormous-sounding it’s positively cinematic, especially on the Bondesque single 'That Golden Rule'. This, it turns out, is no coincidence.

"I’d love to write a soundtrack", says the frontman. "Like Nick Cave and Warren Ellis from the Bad Seeds did The Proposition, and Jonny Greenwood did the There Will Be Blood soundtrack, which was amazing. When you see someone like Nick Cave, who had the mad goth punk hair scoring movies and writing screenplays, that’s really exciting. Anything that takes you out of your creative comfort zone is great. We always try and do that on records. But to do a soundtrack would be amazing, because it’s not all about aural, you’re trying to augment something that’s on the screen. The best soundtracks you almost don’t notice when you’re watching the movie because they’re such an integral part of it."

"Maybe The Hurt Locker", adds Ben. "There’s very little music in that, but it just makes the movie super intense. I think that’s the one I would have liked to have been involved in."

By rights, it feels like Biffy should have reached the point where they’re headlining Reading and Leeds by now. Certainly, their fans are as loyal as any you’ll find, and it’s infuriating to see them leap-frogged for the turgid, uninspiring likes of The Killers year after year. The band, however, seem happy to keep on the slow and steady trajectory that’s kept audiences hungry for more.

"I think we had a rougher time when we were younger", says Simon. "When you first start out you have that unwaverable swagger of being young and making music. We couldn’t believe some of the bands that were doing alright. But I think we worked out long ago that the way we do things might not be the fastest way, but as long as we are comfortable playing, hopefully one day we will headline Reading. If it does happen we’ll be ready for it. There’s always going to be flavours of the month, bands come and go. If we looked at the bill of our very first festival, in 1999, I’m sure the amount of bands that are still going would be about 15 per cent."

"I don’t see the rush", adds James. "Everyone seems to be in such a rush to get somewhere. Why not enjoy what you’re doing just now? We really do enjoy what we’re doing, but we’re not in a hurry."

The record label have high hopes for Only Revolutions, with plans for huge American and Australian tours as well as the next step up the ladder here. But the band – still based in Scotland, with their families around them, spectacularly disinterested in the workings of the music industry and its passing phases – seem bemused by any talk of world domination. The general impression is one of three men at their happiest in their farmyard rehearsal space, making strange noises that sound unlike anyone else.

"We like that things have happened in a natural way", Simon concludes. "We never went chasing anything, trying to achieve something that we saw that someone else had. We’ve always wanted to be the best band that we’ve heard. Every band should genuinely believe that they’re the best band that they’ve heard, otherwise just give up right now. We know that people will come round to it."