Ask the black-clad London teenagers standing outside the Academy, who are prepared to wait around all afternoon for a sighting of the band, and their unofficial spokesgirl will tell you that Fratellis fans "just want to go f***ing maaaaaaad". Tonight's gig will be nothing more or less than a platform for doing so. Nearby in a dressing room, the lead singer and guitarist claims to be looking forward to it as much as those fans are. "There is nothing better," says Lawler, "than being on a stage and playing really loud and seeing people smile and jump around. See here, tonight, it will get to a point where the whole crowd is bouncing. It's brilliant man. I dunno what else music is supposed to do."

It is not necessarily easy to write a pop song as primitive as The Fratellis' breakthrough single Chelsea Dagger, the chorus of which caused the UK to shout along like cave-dwellers who had just discovered harmony. And it does not necessarily follow that the three men responsible for such elementary music are themselves simple-minded. But The Fratellis' determination to please crowds has also inclined them to make a mockery of those who think they could, or should, or must be, more complicated than they seem. Bass player Barry Fratelli has put it like this: "The press are going to make shit up about you, so you might as well do it back."

That remark is typical of the slight defensiveness with which this band go about their business. They began to build a fanbase with that first O'Henry's gig in March 2005. Before they had played even 10 more, their demo tape secured them a contract with the major record label Island. By the time the Scottish media caught up, debut album Costello Music - named after the studio they used to rent above a Chinese takeaway in Budhill, Glasgow - had already been recorded in LA. The Fratellis did not especially require journalistic patronage, and felt no obligation to tell their own story straight.

They would not initially confirm or deny that their name was inspired by a family of moronic criminals from seminal 1980s adventure movie The Goonies. They claimed to have met while working for a travelling fairground owned by Barry's father. Barry himself was said to be a reformed car thief, Jon a nursing home attendant, and drummer Mince Fratelli a lion tamer. Each member knew his rock'n'roll history, and by renaming themselves after their own band, they were not doing anything The Ramones hadn't done 30 years earlier. But The Fratellis weren't trying to create a myth so much as have fun at the expense of those bands, and particularly those music writers, who believe that such myths still have validity.

The true story is not much less compelling for being a great deal more mundane. Barry's actual surname is Wallace, but it really was Fratelli before his mother remarried. A bassist from the east end of Glasgow with over a decade's experience in various groups around the city, he answered an advert in the window of the music shop Sound Control. A guitarist from Paisley called Gordon McRory - later to pick up drumsticks instead under the pseudonym Mince Fratelli - was looking for bandmates to "conquer the world" with. Jon Lawler from Cumbernauld, who had been writing songs through his teens and most of his 20s, was the best other applicant.

They were all getting almost too old for this racket. If rock bands are like street gangs, they tend to seem less of a credible threat as their members near 30. But the flipside of age and experience is that each of them could really play. Each of them saw and heard in the others their own chance to make it. Then Mince broke his back in a car accident, and it looked like The Fratellis wouldn't happen after all.

"That knocked me for six," says Wallace. "We didn't even know if he would walk again, let alone play. Obviously we were gutted for him, but I was devastated because we'd come so close. We were just getting really good, and now we were f***ed. So when Mince came back so quickly less than a month after the accident, McRory returned to the drum-kit in a back-brace I felt like it was a nothing can stop us now' sort of thing."

Last April, The Fratellis released their debut EP. The album followed in September and went straight into the charts at number two on the strength of their singles and live performances. Last month, they were voted Best Breakthrough Act at the Brit Awards 2007. There was, perhaps, an element of sincere vindication in their posturing walk up to the podium, and when Jon said "Thank f*** for The Fratellis", or something to that effect, it sounded as much like relief as triumphalism.

Speaking to me backstage today at the Brixton Academy, Lawler, Wallace and McRory come across as naturally affable people who are also quite intensely conscious of everything they have done to get here. Their enjoyment of all this seems tempered by a sensitivity to the notion that some people might still say, or think, that they don't deserve it. JON FRATELLI aka Jon Lawler

It would be impossible to mistake Jon "Fratelli" for anything other than what he is: the frontman of a youngish rock band. Which is appropriate enough, since it's all he ever wanted to be. His hair resembles a huge puff of black smoke from a failed lab experiment, and his charcoal jeans couldn't be any tighter if he was standing in a wind tunnel. This is not an original look - Lawler's Scottish rock ancestors The Jesus And Mary Chain, among others, pioneered it more than two decades ago - but he's made it his own, in the same way The Fratellis have based their distinct modern sound on a shared familiarity with records from the 1960s and 1970s.

Lawler is recently married, although I only discover this later. He confirms that he is "sort of" from Cumbernauld, having lived there in his formative years before moving to Glasgow, but isn't sure if the fabled ugliness of that new town has any bearing on the escapist antics described in his songs. "I know what you mean, man," he says. "There's a lot of harsh places in this country, and a lot of fun music comes out of them. But it doesn't always work like that. Brian Wilson lived in LA, you know? I wrote all the songs for The Fratellis' debut album in a really shitty place I was living ... "

"Where?" I ask.

"Somewhere between Cumbernauld and Glasgow," he says, apparently amused by his own vagueness. "But anyway, it was a dead sunny month, June I think, and that might be why the songs came out quite happy. There's a lot of fun in them, and no big message. Certain people say that we're dumbing down music, but f***ing hooray, you know what I mean? That's the way it's supposed to be."

Lawler admits he had to write "a lot of bad songs" before any good ones came to him. After leaving school he enrolled on a college music course but dropped out at breaktime on the first morning. "I remember seeing a lot of sums on the blackboard," he says. "I've never been very good at maths."

Until meeting the other Fratellis, he was "completely treading water and trying to work out what I was going to do in life", but writing lyrics all the while. It's possible that Lawler's songs reveal more about his personality than he would ever let come out in an interview. Most of them - including those first singles Creepin' Up The Backstairs, Henrietta, and Chelsea Dagger - seem to be about dubious encounters with strange ladies.

"I've known a lot of dodgy women, man," says Lawler, before changing his tune slightly.

"No, the songs are just fiction. To me it seems a lot easier to rhyme things that aren't true. But maybe I am scared of women. Someone else pointed that out, and I was completely knocked back by it. There was a critique on some website and the conclusion was, This guy is completely terrified of women'. It's probably true. That person might actually know me better than I know myself."

In the earliest days of The Fratellis, it was agreed that Jon would write the songs and Barry would control the band's direction. "Steer us," as Wallace puts it today. "I had a fair idea what to try and avoid," he says. Among the tall tales they have told about their previous lives is the one about Barry being a card sharp. This turns out to be true - Wallace worked for four years as a casino croupier by night, so he could concentrate on music during the day. He had joined his "mate's sister's boyfriend's band" Baby Kingdom at the age of 14.

Realising that he would never be a great guitarist, he decided to master the bass, "because there's only four strings on it". And for the next 13 years, he kept getting better in bands that never became big.

"My thing," he says, "was always just to earn my living playing music, but I was getting to the stage where I was going to give up. When you're nearly 30 and still trying to get mates to come and see you play on a Tuesday, you start thinking that it might not happen like you thought it would. But that's how I knew, when this band came together, it was going to be good."

It is Wallace's experience, and possibly his private resentments, that make The Fratellis so wary of what he calls "lazy journalism", so contemptuous of new bands who "work out what they're going to look like before they even think about musicianship", and so selective in doing what is asked of them by their record label and other interested parties. Jon Lawler has already told me that it's band policy to refuse at least half the requests they receive for "TV appearances and stuff". Wallace, for his part, says he's "proud of the fact that we say no' all the time".

Evidently, however, they said "yes" to a punishing tour schedule that saw them return to the same UK venues again and again last year, which paid dividends when they sold out two shows at the Glasgow Barrowland faster than any other band in history. They have also allowed their song Flathead to be used on an advert for iPod. "Obviously we want our music to be heard by as many people as possible," says Wallace. "The important thing is that the music itself doesn't have to be shit commercial pap. Our stuff is fun, but it also sounds f***ing amazing, and I think it pisses some people off that we're actually pretty good."

For a man with a lot to say, it's a little surprising that his vocal role in The Fratellis is limited to shouting "na na na" type words on stage and on the records. "Yeah," he says. "I have written plenty of songs in the past but when I met Jon his stuff f***king blew me away. I'm not very good at lyrics, or singing for that matter. I try, but I've got a fear of microphones."

I ask Wallace about his mother. What does she think about her ex-husband's surname being made famous by the biggest band in the UK? "That's a long story," he says, making clear that he's not going to tell it. "But yeah, she loves it. She walks around calling herself Mama Fratelli." But does that name function as a kind of alter-ego? Is "Barry Fratelli" in some way an adopted persona?

"No," says Wallace. "It's not as if we're Ziggy Stardust or anything like that. At the time it was just a laugh to name ourselves after the band. It used to be my name as well, so it didn't seem like a big deal to me. But I suppose it might seem a bit wanky now."

The man who now calls himself Mince Fratelli will not speak to me alone. This is not because he is hostile to the press - if anything, McRory seems the most agreeable presence in the band. But he's afraid of being misquoted, because he doesn't like to come across as "nasty" in print. The Fratellis are supposed to have feuded with certain other bands while touring their way to prominence last year, and McRory expects questions on the subject. "I don't want to upset anyone," he says, looking towards his bandmates for support, or confirmation. "I never do. People get annoyed with us, but we don't ever mean it."

The Fratellis, of course, must be McRory's band, given that he's the one who placed the advert that brought them together. "Too right," he says preparing to refer to himself in the third person. "Opportunity of a lifetime ... seeks band to make our mark on the music industry'. Mince's vision will be implemented this year, as we play gigs around the world." His real name may be Gordon, but on the ad he wrote it as "Graeme", because he was in another band at the time, and didn't want them to find out he was making other plans.

It's a measure of McRory's judgement that he realised The Fratellis would be better served if he moved behind the drumkit. But the drums must be particularly hard to play after breaking your back. When I bring up his accident, McRory mishears me. "My accent? You mean because I'm from Paisley?" He won't discuss the crash itself, but explains that The Fratellis' schedule has conflicted with his treatment. "I've got metal stuff in my back that needs taken out. They're going to try and do it in a week or so, but I've missed my last couple of appointments from being on tour."

If you don't actually like The Fratellis' music - the raucousness of which can seem like a forced smile when compared to the seriousness with which they take it - then McRory himself represents a reason to support them. Not because he deserves sympathy, but because he makes fun sound like something worth working, and even suffering for.

"Drumming is quite easy if you practise a lot," he says. "But if you don't, then you get halfway through a gig and wonder why you're doing this. You think your arms are going to fall off. That's what it was like after my accident. Now it's getting easy again. Plain sailing. We just play dead good gigs, and we love it."

The Fratellis' new single Baby Fratelli is released tomorrow. The band play at T in the Park on Sunday, July 8