The night before the three members of Biffy Clyro were due to start recording their sixth album in Los Angeles – "the most important record of our lives" – drummer Ben Johnston went out for a pizza with one of the band's crew. He remembers having one beer, then going to the bar for another, and then nothing until the morning: no memory of anything. In fact, he'd returned to the house that the band were sharing in the wee hours, incoherent and with his face covered in blood.

Neither his twin brother James nor singer and guitarist Simon Neil slept, and in the morning the three of them sat down amid "lots of tears" to decide whether to end the group there and then. "It was black and white," Simon recalls, back in LA where the band are filming a video, several months down the line. "Either the drink stops or we stop. If we'd made a record in that situation we would have been acting, and that's not what being in a band is – and it's not what being friends is. It so happened that the timing of it [on the eve of recording] was so, so bad … but it turned out to be the best thing that's ever happened to us."

"There was no shouting match, I didn't try and pretend I had the situation under control," Ben recalls. "But for the first time, the extent to which my behaviour was affecting everyone – and the future of everything – sank in." He decided to call time on his drinking, and the group disappeared into the Village studio (where, they note, the Rolling Stones, Fleetwood Mac and Slipknot have recorded) to emerge five months later with a double album, Opposites.

It's that rare thing: visceral heavy rock that wears its heart on the sleeve – the sound of a band that's matured without losing touch with the strength of old emotions. Glowing reviews would seem to signal Biffy's ascent into the big time: an appearance on the Jonathan Ross programme and a sold-out show at the O2 in London, and the surefire bet that they'll headline a major festival this summer.

The band have never been an easy sell – starting with their name, which is still a mystery, although its etymology was once attributed to a piece of Cliff Richard memorabilia, a pen or "Cliffy Biro". The world has come slowly to them, and as Simon says, "we've been able to show that we're sincere as a band, and we're not here to become rich or famous, we're here to play music. It helps that we took it seriously from start. We're not chancers, we're lifers."

Biffy are a band who spurn cliches – and, talking to them, it seems the travails they encountered making the new album feel almost irksome. "We never thought we'd ever be the kind of group to have to face that kind of challenge," Simon says, sitting in a beachside hotel in Santa Monica. "We used to laugh at other bands who did."

With a wolfish grin, he adds: "Drinking too much … it's a funny thing for a Scotsman to worry about."

Growing up in Ayrshire, Simon and the red-haired Johnston brothers became friends in the mid-80s, aged seven, and the three always pointedly talk about each other as family. Ben and bassist James's mum ran a nursing home in Kilmarnock while their dad was responsible for building local playgrounds and skate parks – employing his sons to help out in their summer holidays. Simon's dad is a builder, while his late mother, Eleanor, was a police officer.

"There weren't any bands [where we lived]," says James of the band's upbringing. "We never saw success happen to anyone, so we never had any kind of sense of entitlement. There was no one we could compare ourselves to."

Inspired by Nirvana and Guns N' Roses (the glib working title for Opposites was Use Your Illusion III and IV), the band would practise in the Johnstons' garage "and after a couple of years, the boys' mum could hum one of our tunes," Simon recalls. In January 1996, their first gig came at a youth centre in East Kilbride, supporting Pink Kross who had in turn once supported Hole (the band led by Kurt Cobain's widow Courtney Love). "We thought 'Yes! We've fucking made it."

Nothing changed immediately. The industry and media were still feasting on the carcass of Britpop, and for three teenagers in Scotland there was no way of fitting in. "It was the swagger of it all … we were quite shy boys, we didn't have that same arrogance," says Simon.

"[Britpop] lacked emotion. We liked music that came from the bottom of people's hearts," James continues, citing US acts they were now listening to like Bonnie "Prince" Billy and Red House Painters. And as for the next wave to be championed by the music press? "Groups like the Libertines just repulsed us, because they seemed to care more about the perception of who they were as people than the music."

According to Simon: "We probably tried to be cool when we were teenagers, but we called our band Biffy Clyro and that's not cool, we make earnest music and that's not cool. We're not nonchalant, we care too much to be cool."

In 2002, the band released their debut album, Blackened Sky, on the independent Beggars Banquet, which struggled to No 78. "No one was interested in a bunch of Scottish kids with tattoos playing rock music like that," a former member of staff at the label says, adding: "There was a review in the NME that was particularly brutal, which led to some fans ringing the switchboard to threaten the writer – which then made it even harder for them to get in the paper."

Nonetheless, the same source adds, the band never wavered in confidence, growing harder and quirkier on their next two albums, The Vertigo of Bliss and Infinity Land. With the benefit of hindsight, Simon says now that "in some ways it was a defence mechanism – making things hard to like gave us an excuse if people didn't like them".

For their fourth album, the first on a major label, there was a recognition that to move forward, they had to simplify everything. That decision coincided with the death of Simon's mother (from complications following previous heart surgery) while he was away on tour. The result, Puzzle, was their most emotionally direct record yet – especially Folding Stars, which lamented "Eleanor, Eleanor, I would do anything for another minute with you".

It was a dark time for the singer, who has said that he spent "weeks – weeks – in my bed" not wanting to get up. But the album went to No 2 and was voted best of 2007 by Kerrang!. Support slots for Muse, the Who, the Red Hot Chili Peppers and Bon Jovi ensued, and a fifth album, Only Revolutions, was released in late 2009. Six singles came from the record – including the exhilarating Mountains and Bubbles (which perfectly represent Biffy's command of rock dynamics) and Many of Horror, a record that showcased Neil's grasp of balladry so well that it went on to enjoy an ignominious afterlife. Retitled When Worlds Collide in a cover version by 2010 X Factor winner Matt Cardle, it topped the charts that Christmas.

"We were on tour in Australia, when it happened, and thought it was weird enough to be funny," Simon recalls. "It was only when we got home that we worried if it was a terrible thing. But it felt nice to infiltrate things our way. We haven't gone begging to any fucker ever. People have always come round to our way of thinking. And I have to say my mum would have been over the moon about a Christmas No 1!"

In an increasingly corporate musical culture, Biffy's stance on selling out sounds almost archaic. "I'm dreading someone like Coke offering us half a million quid to do something," Simon says, even though he does acknowledge that as label mates on Warners with Bugs Bunny, they're scarcely an underground outfit any more. James insists there's just one company for whom they'd write a song: purveyors of that Caledonian nectar Barr's Irn-Bru.

Few groups remain so grounded: the three of them still live in Ayrshire, as Simon says, "within an hour of each other at all times". "That makes it sound so sinister!" James exclaims, but as he says: "We've grown together, we've become men together."

Last year Ben got married, and James is in a long-term relationship. "My money's still my own!" he laughs.

Simon has been married for five years – his wife is a secondary school teacher. Inevitably she is pestered by pupils for tickets to Biffy shows. But as he says "it's a working-class town and people there are very down to earth ... and people respect teachers in the same way they do doctors or nurses."

"And besides," he adds, "she's strict. 'Don't you be asking that again young man!'"

Domestic life has, though, conflicted with life on the road. In particular, after two years of touring Only Revolutions, Ben's drinking was becoming a problem. "I'd never get up and start drinking through the day," Ben says. "I was never hiding my drinking. I just didn't have a stop mechanism. It confused me because I'd be drinking and have a blackout, even when I thought I couldn't be in blackout territory. It started to happen more and more."

"I hope you don't mind me saying this," Simon says, looking across the table at James before returning his gaze at me, "but for about two years Jim has suffered incredible depression because he blamed himself for what was happening to Ben, he thought it reflected on him somehow."

The band had returned to Ayrshire to help recover, but Simon also faced the grief of his wife suffering a succession of miscarriages. "It was really tough ... it didn't put a strain on our relationship, it was just the strain of life: life can seem pretty formidable at times," he says.

With the band "it felt like we were losing that connection we'd had all our lives, and my private life was getting on top of me, so it was like 'I can't turn here, because it's so tough', but then, the band ... I can't turn there because we're not quite seeing eye to eye."

Instead he pushed himself into the writing of the new record. The result was a group of songs that dealt with these bleak times, and then a further set that saw him turn a corner and resolve to make things better: 40 tracks were whittled down to 20 and split into two discs to reflect the way in which "life deals you good and bad hands".

I point out that making a double album sounds a funny way to deal with the pressure, but Simon says it's simply a reflection of an enduring work ethic. "Our parents were out grafting six days a week when we were growing up. There is something quite Calvinistic about it – it instils something in you."

On the other hand, it's also a record that often revels in a far more Celtic sense of abandon. "The songwriting process needs to remain completely pure. I try and remain a total teenager in that regard. We all do. 'That feels fucking good, man! Let's go!'"

Ben promised to cut down on drinking (he switched to white wine spritzers as part of his plan), and the band headed to LA, where they had recorded the previous two albums. Then came that fateful night.

"I was being told about all this shit that had happened and I'm thinking 'Holy fuck! How did that happen?'" Ben recalls. It's still not clear whether he'd been in a fight or cut his ear falling into a bush, but whatever happened, it proved a turning point.

Simon produced his ultimatum in the cold light of day. "I felt like we'd resolved things at home," he says, "but perhaps we were too chickenshit to really confront the problem. We're men! We were skirting around it. But after that night, we had a decision to make. After everything I'd gone through with my wife as well, I wasn't going to waste 15 years of my life. It was a chance to take control of my life – and to try to guide this ship homewards. It was 'let's fix this...'"

The irony was that the songs on the record they were ready to make addressed that state of mind already. The band hit the studio after all, and threw themselves into five months of recording with renewed purpose. In fact, Ben, who had joined AA, played better than ever – "partly because I was sober," he says, "and partly because I knew I had something to prove."

"It made us all up our game," says his brother.

LA had other benefits: in their beachside house, the band worked their way through prodigious quantities of weed thanks to Ben's easily procured medical marijuana card. And flights of fantasy that they might never have contemplated in the gloaming of Ayrshire were more easily entertained.

"Hiring a mariachi band to record a song can feel a bit extraneous if you're thinking about when to pay your council tax," Simon laughs. "But in La-La Land you can do things that at home would feel completely ridiculous. You can take risks without someone saying 'What do you think you're doing? You're mental.'"



It's a month later when I see them again, albeit briefly. The promotional treadmill is in full whirl but after a Christmas spent with their families in Scotland, the band are once more an easy-going delight to spend time with. (Perhaps especially because James is also now engaged to his girlfriend.)

The rest of 2013 will see the band tour the world, but according to Simon they're already looking beyond that. "For the next three records we're going to change the way we operate," he says. "This is the last of our big rock trilogy – the first three albums were wonky rock records and the last three have been really big and bold, but now we're going to tweak it all. It's important to force a change because we want to be doing this for the next 20 years."

In fact, the singer adds, he'll probably not listen to Opposites again now. Nonetheless, the three allow themselves a final moment of reflection.

The final track on Opposites is called Picture A Knife Fight, and without wanting to ruin the delight of the narrative arc, it ends with Simon screaming, exultant, "We've got to stick together!" to the blisteringly loud sound of crashing drums. It's enough to warm the heart of even the most cynical.

"You've got to feel the belief in each other and to feel the love, and if that starts to dissipate at all then you're in a real bad place," Simon says.

James sums up what an X Factor judge would probably call their "journey".

"If you're that invested in each other's lives, shit can happen because anything you do affects everyone else," he says.

"But we've turned things around and the feeling of pride we have of being together is immense. We feel we can take on the world together. We've got it together and it feels really strong."

Opposites is released on 28 January