THE doors of the tour bus hissed open. Jon Lawler stumbled down the steps. The desert heat walloped over him like a heavy blanket. Over there, low mountains and skinny palm trees. Around him, clouds of dust kicked up by the wheels of the other bands' travelling accommodations (was the Kaiser Chiefs' bus bigger than his bus?). It smelt like… California. And it smelt like horse dung, for these fields belonged to the Empire Polo Club. And jeez, it was baking.

It was the Coachella Festival in April last year, and it was a show too far for the Fratellis' frontman. "We did our gig on the Saturday afternoon. Then I ran away. Flew back to Britain. And me and my girlfriend went to Malta on holiday. I don't know why."

What Lawler means is, he doesn't know why he wanted to go to Malta. He does know why he legged it: the Fratellis had been touring for well over a year and they were shattered. I'd seen them the previous spring, also in America, at the March 2006 South By Southwest Festival in Texas. It was their first US show: outdoors in a bar, next to a barbecue hosted by their record label as an introduction to their smart new charges from Glasgow. A meat and greet, if you like.

Fast-forward one year to Coachella and the trio with the stonking line in muscley, shouty pop have gone stellar. The Fratellis' debut album Costello Music sold 1.5 million copies. They progressed hard and fast from small NME-endorsed shows and the music weekly hailing them the "best new band in Britain". There was a landmark gig at T In The Park, a full-on rammy in the New Bands Tent. Support slots with Kasabian and The Police. Four sell-out nights at London's Brixton Academy. A triumphant homecoming at the SECC. Hit singles that defined the summer (and autumn and winter) of 2006 and 2007: 'Henrietta', 'Creeping Up The Backstairs', 'Whistle For The Choir', 'Chelsea Dagger'. The latter is that rare thing too: a bona fide terrace anthem, beloved of the crowds at Celtic Park, Love Street and Stamford Bridge.

Forget Scouting For Girls, The Wombats and The Pigeon Detectives: when it comes to crafting huge, 'event' songs to wow an occasion, only The Proclaimers can match the Fratellis. This is People's Music. And the punters kept voting with their feet and fingers: at last year's Brits, the Fratellis won the award for Best British Breakthrough Act, as voted for by Radio 1 listeners.

But living life at that kind of speed, things are bound to get a little frayed. Hence Lawler scarpering at Coachella.

"It's not that things had been going bad – it was just one tour too many," he says. "We f***ed off two weeks' worth of shows. But after sitting at home for three days I was desperate to go back. We went back (to the US] three times after that. Everything was brilliant. I loved the whole summer."

One year on from Coachella, the Fratellis are in London, in the BBC's Maida Vale studios. They're recording a session for Zane Lowe's Radio 1 show. Drummer Gordon 'Mince' McRory is sweating as he goes through his paces. Bass player Barry 'Baz' Wallace mooches about, waiting for the recording engineer. He named the band they formed in April 2005 after they came together via a 'musicians wanted' ad in Glasgow instrument shop Sound Control; seemingly Fratelli was his mum's second name from her first marriage. Lawler sits in a lounge area strumming on a guitar. Next to him, reading a celebrity mag, is his wife: a sometime burlesque dancer, Chelsea Dagger was originally her stage name, he says; they married last year.

Lawler is in chipper form. He speaks in a broad Glaswegian accent that manages to be both clipped and drawled. The Fratellis are midway through a run of low-key shows. After six months off the road, they need to warm up. And they need to get the fans up to speed with the songs from their new album, Here We Stand. That shouldn't be difficult: the Fratellis' second album is like their first, only more so: huge, swaggering pop songs, instant singalong classics. But now with added rock'n'roll piano.

Its confidence – its loudness – is all the more surprising considering the Fratellis produced Here We Stand themselves, in the new studio they've bought with their manager in a former janitor's house in Glasgow's West End.

"When we made Costello Music we'd only been together nine months or so," he says. "In that time we'd only done 25, 30 gigs. That's not really enough to decide how it is that you sound. After you've toured for two years, that's when you end up becoming the band you're gonna be. So Costello Music didn't sound like us any more. I thought we'd got naturally heavier. And the songs we ended up writing for this one leant more in that direction."

He's not wrong: lead single 'Mistress Mabel', already exploding all over daytime radio, is the confident, polished big sister of one of the 'character' songs from Costello Music. It sounded great when they played it on Later… With Jools Holland last week (with supporting 'colour' provided by Lion Rampant flags tied to the drum kit and the legend 'Nae Danger' sprayed on an amp).

Lawler is never one to shy away from speaking his mind – he says 'Mistress Mabel' wouldn't have been his choice for first single, but he understands why their record label have opted for it. "It's them erring on the side of safety," he says.

No matter, Here We Stand is thick with potential hits. The opening 'My Friend John' is a galloping rock'n'roll number, and 'A Heady Tale' has a piano riff that'll have fans bouncing at festivals all summer – expect a good-natured riot at this year's T in the Park when they will be second from top on the main stage on the Saturday.

"I'm really proud of how 'A Heady Tale' turned out," he says. "I couldn't see anyone taking that kind of chance with that kind of bar room piano. It's not really that trendy just now is it? I hear plenty indie slow ballady piano. But I don't hear big piano slides. But 'Stragglers Moon' is probably my favourite song on the album. I can't hear anyone else in our league coming up with that song. It's definitely got a Floyd or Beatles edge to it. We're really big Floyd fans. I think the whole record has got that ambition in there."

For the Fratellis it is, again, about moving forward, and fast. This has meant them banning the ubiquitous 'Chelsea Dagger' from use in certain areas: football round-ups are fine, but they said no to the Hollywood producers of Shrek 3 and Forgetting Sarah Marshall, both of whom wanted to use it on their films' soundtracks. But other marketing opportunities are fine: 'Flathead' was used on an iPod advert, and (bizarrely) 'Got Ma Nuts From A Hippy' helped flog Burberry Perfume. "And (lubricant manufacturers] Pennzoil wanted to use 'Chelsea Dagger' for an advert in Texas. They offered a sh*tload of money. I thought, I don't care that much, and who of my mates are gonna hear it? We get a bit of abuse for stuff like that. But we're not a f***ing charity!" the 29-year-old laughs. "Sometimes the money's just too good to turn down.

"We're not completely whoring ourselves," Lawler adds. "We know what will do us good."

Too right. Writing a second album full of blistering pop songs will see the Fratellis right as well. I hope they're prepared for another 18 months of brain-scrambling touring.

• Mistress Mabel is released May 26, Here We Stand is released June

• www.thefratellis.com