TRY TO get your head around this one. You grow up in Glasgow, you love old-style rock'n'roll and Elvis Presley is one of your idols. You write a song called Daddy's Gone about your childhood memories of your absent father. It creates a bit of a buzz as a demo single and can be heard across the world on the internet. On the other side of the Atlantic, an American woman listens to the song and it makes her think about her own childhood and her absent father. She likes it so much that, when she's on a family holiday in Scotland, she calls you and asks to meet up. Her name is Lisa Marie Presley.

Such is the surreal explosion of circumstance that has become daily life for James Allan and his band Glasvegas. "Lisa Marie got in touch before we'd signed a record deal, basically just to say, Hiya, I'm Elvis's daughter', that kind of thing," explains Allan. "She and her husband and Priscilla came to see Led Zeppelin in London, and then they came up to visit Scotland because Lisa Marie had never been before. So she phoned and asked if we wanted to meet up for a drink. We went from the studio and met them and just had a night out, you know? They're just normal, sweet people."

It might seem bizarre that the 28-year-old singer can be so down-to-earth, taking such a peculiar turn of events in his stride. He's certainly not trying to act cool for effect, nor is he striving to appear cynical or blasé. It's just that, when your world has turned upside down so spectacularly in a matter of months, how should you react to the knowledge that the daughter of an all-time hero has been affected by a demo you recorded in your east end bedroom?

Two years after forming, Glasvegas are on the cusp of something very big indeed. Named "the best new band in Britain" on an NME cover a few weeks ago, with their first proper single, Geraldine, going straight into the charts at number 16 last weekend, fresh from playing to the biggest crowds of their career at the Glastonbury Festival, Glasvegas should be wearing arrogant hearts on champagne-stained sleeves. But that's not the kind of people they are.

When I catch up with Allan - the afternoon after Geraldine's chart success is confirmed - he is hampered by a cold and fairly knackered, to be sure, but his answers are thoughtful and considered. He might sometimes struggle to articulate the abstract ideas in his head, but he knows what he means and knows that it matters. Notions of fate and luck come up a couple of times in conversation, as does an unadorned honesty about the personal experiences Allan tries to get into his songs. For all of the black clothes and on-stage sunglasses, the Johnny Cash hair and the Joe Strummer looks, I get the feeling that he's a genuinely sensitive soul.

Allan set up the band in 2006 along with his cousin Rab on guitar, Paul Donoghue on bass and Caroline McKay - who worked in a vintage clothes shop they frequented and had never played an instrument in her life - on drums. A handful of demos and limited release singles won them a fervent local following and the thumbs-up from the music press. In February of this year they signed a deal with Columbia Records and have just put the finishing touches on a debut album recorded in New York City.

Everything about Glasvegas is a clash of opposites. The band name, for instance, is part industrial hometown, part American neon-lit glamour. And the music takes the sweet melodies of classic US rock'n'roll, Motown and 1960s girl bands, then fits them over distorted guitars that owe more to the Jesus And Mary Chain and My Bloody Valentine. Then there are the lyrics, which use those pretty tunes to deliver Allan's experiences of school playground fights (Go Square Go) and park kickabouts (Daddy's Gone) in an uncompromising Glaswegian accent. When played live - usually in intense, half-hour sets swathed in red light - the songs form a veritable wall of sound that exists somewhere on the darkest outer limits of Phil Spector's imagination.

The lyrics are the key to what sets Glasvegas apart from other emerging bands in 2008. You can be sure that no other single in the current Top 20 is told from the viewpoint of a social worker ("When you say that I'm no good and you feel like walking/I need to make sure you know it's just the prescriptions talking") - with the added twist that the Geraldine in question is now the band's tour manager and T-shirt seller.

Allan doesn't call them lyrics, however. To him, they're "poems" - a word that seems to carry more personal, more intimate baggage. In fact, his observations of working-class life are more in tune with the novels of James Kelman or the short films of Lynne Ramsay than anyone on the Scottish music scene. On the track Flowers And Football Tops, for example, he touches on the murder in 2004 of Glasgow teenager Kriss Donald, although the words are filtered through the eyes of an anguished parent who realises that their child will never come home again.

"I've said from the start I didn't base that song on Kriss Donald," Allan points out. "I would never write a song about that boy unless I'd asked his family. I wouldn't insult anybody by trying to write a song about that. It was inspired by seeing Kriss's mum and other people's mums, like those girls in Soham. Time after time you're seeing these bairns, and it just kills you, totally kills you It kills me to think about how my mum would handle that, how heartbreaking and terrible that would be. You put yourself in other people's positions and imagine how that would be, whether it's through somebody's fortune, like winning the lottery, or through tragic circumstances."

Empathy has formed the basis of several songs, including Polmont On My Mind. This track, about how a prison can etch itself completely onto an inmate's every waking hour, came about when Allan met a man who had been sentenced for manslaughter after he kicked and accidentally killed a guy who was in a pub fight with a mate.

"It would be quite naïve to think that that couldn't be me," the singer says. "A lot of people look at folk in prison or who are homeless, and they think that's not their world. They don't realise that they're only one or two steps away from it being them."

Allan practises what he preaches and, about a year and a half ago, Glasvegas played some gigs in Scottish prisons, taking their songs into Saughton, Cornton Vale, Barlinnie and Polmont. "I think it was quite emotional for the prisoners as well," he remembers. "They were some of the most real gigs I've ever played, and I don't know if I'll ever match that again in a lot of ways." It's more than a Johnny Cash affectation, then.

As Glasvegas's fan base grows, it must be strange for a man so closely connected to his lyrics to see a crowd take those words, sing them back at him and take ownership of some of his most personal memories.

"The first ever time that happened to me," he says, "a drunk guy came up to me in a pub and started singing part of Daddy's Gone in my face. At first it made me feel quite uneasy. I mean, I could understand why people would go to a pub and sing something like Cigarettes And Alcohol by Oasis or I Love To Boogie by T.Rex. But I couldn't understand why somebody was singing one of our songs. We've played gigs in Scotland and England, and audiences know the lyrics, probably from the demos. For some reason, they sing them like it's an anthemic thing. I don't get freaked out by it now. It's a beautiful thing, people singing your poems."

MUSIC wasn't Allan's original career choice. After leaving school, he joined Falkirk Football Club on a youth training scheme in 1997, playing for a couple of years as a left winger. After that, he took to the field with a number of clubs - Dumbarton, Stirling Albion, Cowdenbeath, Queen's Park and Gretna - but it never quite worked out. Still, Hampden's loss is Barrowland's gain. And like a star striker who scores the equaliser in a cup final only to miss during the penalty shoot-out, Allan knows that his current career is a succession of highs and lows.

"When we were in the New York studio, it was quite isolated and there were lots of times that I doubted whether I would get the ideas and sounds that were going on in my head down onto a bit of plastic. But then I'd go in the next morning and the grey skies had moved away. You hear the work you've done and it becomes clear that you have executed what you set out to execute in the first place. I went from self-doubt to euphoria - there's not really any in-between. That's the bittersweet thing about rock'n'roll, but it's what you sign up for."

Songwriting is a process Allan finds difficult to describe. In fact, he can't even put into words his original concept for the band, describing it as "not so much about melody or lyrics but a certain colour, although I can't explain what shade the colour was". The colour he talks about, despite the band's public image, is not black. James Allan might appear moody and intensely focused on stage, but get him talking about his next planned project - a Glasvegas Christmas album - and he lights up like an electric Santa hanging off a bungalow roof.

"Christmas is the time of year when everybody takes stock, isn't it?" he muses. "And sometimes you can really freak yourself out because you think about where you're at in life, or where you're going, or where you've been over the last year. But Christmas can be a romantic time as well. I've always found Christmas such a magical and exciting time of the year. The snow is so twinkly and beautiful because of all the lights and stuff. All those things and all those moods: that's what I'm going to try and capture on the record. I can't imagine that it's going to be like the Phil Spector Christmas Album, which is maybe my favourite album of all time. The plan is that we go to Transylvania and record it. We've been looking at cathedrals and some places that look like Castle Greyskull "

Can James Allan match Elvis's Blue Christmas with his own yuletide composition? Lisa Marie probably thinks so.

Glasvegas play T in the Park on Saturday and Hydro Connect on August 30