Math rockers with an appetite for destruction: Foals gallop up the charts

The band have an intellectual hinterland – but they like a bit of chaos. So can their sound survive domestic bliss? As they set off on a new British tour

Café society: Jack Bevan, Jimmy Smith, Edwin Congreave, Yannis Philippakis and Walter Gervers of Foals

For all the disappointingly polite, middle-class rock bands you meet in this job, who tell you that their tour bus is a civilised haven, involving tea, digestive biscuits, and DVD box-sets, it's refreshing to meet a band for whom touring is just as unruly as you'd imagine.

"It's 24-hours, seven-days-a-week, just absolute, untrammelled carnage," states frontman Yannis Philippakis, who is well known for clambering on stage-monitors and hurling himself onto the young, heaving crowds. He goes on: "The way that we play shows requires getting to a heightened state that then, after a show, has to be let out. Usually that's when the trouble occurs." He recalls such trouble – a show in Vancouver at the start of their last US tour which resulted in a letter of warning forwarded by the Canadian venue to every venue down the American West Coast. "I swear you weren't kicking a security guard in the head while we were playing," he says, facing guitarist Jimmy Smith. "There was all sorts of stuff that they definitely made up… Or at least I can't remember happening. We don't have NutriShakes and go to bed early, put it that way."

In person, Foals are intense and brooding. Live, that intensity translates to feral; ferocious attacks on their guitars in performances that buzz and effervesce with energy. Next month they play the Royal Albert Hall, but it's the tiny, cavernous XOYO in the back streets of east London, throbbing with pogoing fans, where they played a secret warm-up gig this month, that's their more natural habitat. When I first saw the frenetic guitar band, it was at the tiny Buffalo Bar in north London in 2007 – long before the release of their debut album. Amid the hype, it was clear that their focused energy and distinct polyrhythm-driven math-rock would lead them to big things.

Since, the band have achieved a Mercury nomination for their 2010-released second album Total Life Forever, two Top 10 albums and are now celebrating their highest-charting album with Holy Fire (a No 2), while their Albert Hall gig sold out in 10 minutes and their single "Inhaler" racked up 2.5 million views on YouTube. But when the band began, after four of the five quit university, including youngest band-member Philippakis after a year of English literature at Oxford, it wasn't with fame in their sights. "It might sound disingenuous to say this, but there really wasn't," says Philippakis. "We were a ramshackle punk outfit playing house parties. It's not like we come from slickly corporate real go-get-'em type backgrounds. We're slackers from Oxford that spent a lot of time listening to records, being nerdy and smoking pot and being left off the sports team, and that's where the band came off."

Ramshackle they may have been, but there has always been a serious work-ethic and high quality-control to the band that have, at their helm, a perfectionist for a frontman. Philippakis, the 26-year-old son of a South African academic (his mother) and a Greek architect (his father), has a reputation for being a spiky interviewee, but when I meet him with Smith at a north London cafe near their home, I find a man who's complex and opinionated, fiercely intense and intelligent, sometimes pretentious, and keen for his band's music to be understood. After their 2008 urgent math-rock debut Antidotes and its 2010 follow-up, the muscular, direct Holy Fire sounds their most relaxed album to date.

"It's definitely the least encumbered by thinking. It was much more of a gut and spleen record than anything else we've made," says Philippakis, adding by way of an explanation: "Maybe on Total Life Forever there's a feeling that we were allowed to wormhole a little bit too much and it became too introverted and lethargic. At heart we're an energetic band, we're a live band, and I think there was something clear-headed about this record." It was also the time for Philippakis – creator of abstract lyrics – to explore more personal writing.

"I felt there was something cowardly in remaining in a place lyrically where it was easy to obscure sentiment and I wanted to push myself to write from a place that felt emotionally exposed and sincere," he pontificates. "In order to be able to play a song night after night, for it to mean something to other people, it has to be genuine."

The sense of liberation in the album is partly due to its producers Alan Moulder and Flood, whose north-London studio they packed with £400-worth of plants – ferns, ivy and creepers. "It made the space our own; sometimes you can go into the studio and the vibe can be tainted by who's recorded there."

But there was also the contentedness and confidence the band felt when making the third album. Having lived together as a band in Oxford since their inception, that Philippakis and Smith both recently moved in with their girlfriends – and each other – has prompted the ever-questing frontman to wonder if this could be a negative move. "I do worry about becoming too content", he says. "It's like magnets that repel – you can't have a fully balanced and contented domestic lifestyle that's full of the joys that that brings, and then be able to write records that have power to them. I don't know how we would do that. I think there's a certain amount of creativity that's predicated on being alone or being melancholic. It's like: 'Do I take the blue pill or the red pill? Do I have this rosy future with like a Buddleia and two grinning kids? Or a life where you don't have that, but what you do have is the ability to keep making art?'"

Philippakis took up a vast array of interests to balance his frenetic touring life. He went back to Greece, to see his father, and also to escape. "It's just a great place to go to when you need to get away from something", he says. "The landscape is beautiful and raw. It's got a primal power to it; it's sheer cliffs and wild ocean." And he took up gardening and the challenging task of growing roses.

"It's something grounded to make you feel normal. I like growing things. It just feels like the perfect counterbalance – it's private, like a sanctuary, away from the traffic and the smog." And with that they're off, back into the traffic, and the smog.

'Holy Fire' is out now. Foals tour from 2 to 28 March