Rocket man: How does Elbow's lead singer Guy Garvey remain so down to earth?

Men with beards, the five members of Elbow shuffle unassumingly on to the stage at London's O2 Arena to the deafening cheers of a crowd that clearly obsesses over their favourite band the way 14-year-old girls do Justin Bieber. It's a winningly incongruous sight: lip-quivering admiration for five blokes who, though they may dress in Liam Gallagher's sharp Pretty Green label, nevertheless look more like his shambolic uncle than they do his peers.

But with Elbow, it's all about the music, and the music is wrought and majestic and far too subtle, strictly speaking, for enormodomes such as this. Over the next two hours tonight, on this cold March evening, the mood they elicit from these 10,000 thirtysomethings is one of slack-jawed awe, the goosebumps frequently giving way to actual tears. It is this collective outpouring of emotion that lends added poignancy to singer Guy Garvey's regular query from the stage: "Is everybody OK?"

And if Garvey seems a little unsteady himself from time to time, swaying on his knees and tripping over the occasional lyric, there is good reason. The man is drunk.

"Oh, evenings like this are overwhelming, really," he will say afterwards. "If I didn't have a drink or two before the show, and, OK, another couple on stage [at one point between songs he mixes cocktails for the entire band], you'd hear it in my voice – the nerves, the terror."

But he is learning, gradually, to overcome this.

"We've been doing this for a long time now, 20 years. To have reached a point where we know we are among friends is – well, it's nice, it's really nice." k

Two weeks later, and Elbow are appearing on the BBC show Later with Jools Holland to promote their new single "Open Arms". It's the kind of unifying anthem they do so well, and one that will likely prove a highlight when they perform it at Glastonbury at the end of this month. Later... is filmed live, and the band are due on at 10.20pm, closing the show with a climactic performance featuring Manchester's Hallé Youth Choir on backing vocals.

But there comes a problem. The act on before them is a seasoned old cove called McCoy Tyner, who, once his band get into the groove of their interminable jazzy noodle, don't know how to stop, and so they don't. They simply play on, Holland incapable of interrupting their flow. When the floor manager finally steps in to do so for him, the camera pans hurriedly over to Garvey, caught unawares and gaping, convinced that their slot has come and gone. He quickly composes himself, and the band hastily begin. The fact that they are permitted to play their song in full very likely upsets Jeremy Paxman, whose Newsnight is delayed by four minutes as a result.

Garvey is laughing afterwards. "We're used to cock-ups," he says. "They always seem to happen to us. In fact, for years we believed we were cursed. Whenever something was about to go right for us, it always seemed to go wrong instead..."

The televisual cock-up is repeated just three weeks later. They are in New York where they have geared a week's worth of promotion around what many believe might just prove their tipping point in the US: an appearance on the Late Show with David Letterman. But the chat-show host's last guest runs over, and suddenly the credits are rolling. The producer breezes in to their dressing-room afterwards. "Sorry guys," he tells them. "Next time, OK?"

If the band that first got together in 1991 had got rather used to the black curse, then they have also become acquainted with an abrupt reversal of fortunes of late. Since 2008, things have started to go right for Elbow, and everybody now, it seems, has a soft spot for them. They are the People's Band, its frontman the recipient of the kind of plaudits once reserved for Stephen Fry.

He blushes. "Ah, but that won't last. Pretty soon I'm sure it'll be: Guy Garvey? Gobshite."

Elbow's evolution has been slow, and somewhat tortured. Though they formed while still at college, it wasn't until 2001 that they started releasing records, their music slow and melancholic, broody and sinister, and redolent of early Peter Gabriel and Talk Talk. They would never compete against Oasis for the number-one spot. Their first album, Asleep in the Back, was nominated for a Mercury Award. This, and its 2003 follow-up, Cast of

Thousands, both shifted 150,000 copies and certified them, if nothing else, as cult stars. The rambunctious Leaders of the Free World (2005) was mooted by many as their major-league breakthrough – it contained songs that sounded like hit singles – but their then-record company imploded, taking them down with it.

"It was touch-and-go for us after that," Garvey says. "We were funding the next record ourselves, and we'd almost run out of money. We didn't even know whether it would see the light of day."

But this is where their story became, in Garvey's words, "a fairytale". That record was The Seldom Seen Kid, whose songs quickly made their way out into the world in a manner previous songs hadn't. Soon after its release, GMTV's Lorraine Kelly – not previously considered an astute music tipster – publicly proclaimed a love of the album track "Mirrorball", and by the time "One Day Like This" was released as a single, its euphoric uplift soundtracking endless TV shows to the point where it became, ostensibly, our new national anthem, Elbow were a sensation. When he appeared on the Andrew Marr Show one Sunday morning, Garvey found himself cornered by another of that day's guests, the then-prime minister Gordon Brown, who also revealed an admiration for it. "Though he did call it 'On a Day Like This'," the singer points out.

The Seldom Seen Kid went on to sell a million copies, and won that year's Mercury Prize. Two years on, and fifth album Build a Rocket Boys! has cemented their position as one of the most loved bands of their generation. The sense of goodwill now coming their way, Garvey acknowledges, is palpable.

"But I'd hate anyone to think I was pushing this genial, down-to-earth, working-class thing," he says, suddenly k anxious, and scratching at his whiskers, "because I'm not. We appreciate the goodwill; it's not lost on us. We are grateful for it, enormously. And until everybody does decide I'm a gobshite, we plan to enjoy it."

Guy Garvey is 37 years old. He looks older; a big, bearded fellow with a careworn, lived-in face given to easy smiles. His demeanour is avuncular and genial, which is very anti-rock star, as is his dress sense. He rarely leaves home without his university-lecturer-like suit jacket, while his shoes, which look like hillwalkers, are unashamedly scuffed. He is an avid bird-watcher, and rolls his own cigarettes, which he smokes while wincing.

We meet on a sunny day in Manchester in early May, in the beer garden of one of his favourite local pubs. He is halfway through his second pint when I arrive. Elbow bassist Pete Turner is with him, but soon makes his excuses. He hugs his bandmate in farewell, and, because they very likely won't see one another until tomorrow, deposits a fond kiss to the top of his head.

This is a very Elbow thing to do, a public display of fraternal kinship. It forms the basis of so many of their songs.

"My mates have always hugged and kissed each other without any bashful awkwardness about it," Garvey points out. "I didn't realise that saying something like 'Love you, mate' in a song was particularly unusual or revolutionary until people started suggesting it was."

When he was 13, Garvey, the son of a trade unionist and one of seven siblings, abruptly decided that schoolwork no longer suited him. And so he effectively downed tools. "At the time, I used my parents' divorce as an excuse," he says, "but I'm not sure how true that is. They were amazing parents; still are. But whatever the real reason, schoolwork stopped appealing to me." Far from the stereotypical bad lad, however, he didn't play truant. "No, I still went to all my lessons, and I contributed in class, but I never did homework, never handed anything in."

At 16, he was ready to quit education altogether, but his older sister thought otherwise, and enrolled him into the local college where he quickly gained a reputation as something of a show-off. He rarely passed up an opportunity to get up on stage and sing. Fellow students Mark Potter, Pete Turner and Richard Jupp asked him to join their fledgeling band, Mr Soft. Soon after Potter's brother Craig arrived on keyboards, they had rechristened themselves Elbow after a line in Dennis Potter's The Singing Detective, in which "elbow" was pronounced one of the English language's most sensuous words.

They then went about launching their career at a snail's pace, mostly happy to remain a tight, insular unit making the kind of music that pleased, first and foremost, themselves. "Did we ever imagine we'd break through?" Garvey wonders now. "Not really, no. I can still vividly remember supporting U2 at Wembley Stadium a couple of years ago in front of 90,000 people, and feeling convinced that there had been some kind of mistake. Still do, in fact..."

In a music world dominated by at least the illusion of skyscraping confidence, Garvey is notable for wearing his sensitivity on his sleeve, and for articulating it with uncommon grace. He thinks a lot, possibly too much, and as befits someone who appears older than his years, the theme that runs through Build a Rocket Boys! concerns the vagaries of ageing. He's not even 40, yet is already fearing middle age.

"As you get older, different insecurities come to the fore," he ruminates. "One fear disappears, and another comes to take its place; you can only have a certain capacity for happiness, sadness, remorse and fear at any one time, and mine change all the time."

A current worry is that, professional success aside, he might have become the kind of man his younger self would have sneered at. "My girlfriend [Emma Unsworth, a journalist turned full-time writer, whose debut novel is published this month] and I have just bought a house, with a little patch of land," he says. "We want to start a family. It's the most important thing in my life right now, and that's a good thing, it definitely is, but at the same time I worry about it. I mean, is this what I've become? A useless suburbanite who talks about his new house, and who fears the younger generation because they go around in hoodies?"

Until recently, he had harboured ambitions to up sticks and move to New York, but for various reasons has now decided to stay put. Like a particularly loyal dog, Garvey sees Manchester as his turf. When he strays, he becomes discomfited, lost.

"I do like to be around friendly faces, it's true," he says, "and I get no bigger kick than hanging around with the people I've always hung around with. The rest of the band have kids already, and they are excellent, excellent fathers. Watching their kids grow up, and having a stake in their lives through association, is pretty overwhelming stuff. I wouldn't want to be apart from that. And we want to have a family here, now, in Manchester, nowhere else. That's why we've delayed New York. New York can wait. It'll still be there when we're older."

Besides, he has much else on his plate right now. In addition to the band, Garvey has a regular Sunday night slot on BBC 6 Music, and he has also started making documentaries for Radio 4. A recent one was entitled The Honest Musician's Fear of Accidental Plagiarism, prompted after he unwittingly lifted a line from somebody else's song and passed it off as his own (he later apologised to the artist in question, "and I bought him a pint to make up for it"), and another was called The Rainy City, in which he studied the relationship between Manchester's weather and its creative output.

"I enjoy doing them, and would like to do more, but I've got to be careful," he says. How so? "Well, I saw that Nick Cave film recently, The Proposition [Cave scripted it]. I got to meet him shortly afterwards, and I told him I'd been anxious before seeing it. He asked me why. Well, I told him, I have a book of Lou Reed's photography, and it's shit. In other words, you've got to be careful not to do things just because you are allowed to. There's no excuse for making dross. I wouldn't ever want to do that."

It is early evening now, and Garvey must leave. He has a dinner party to prepare, something his younger self would no doubt consider a typically useless suburbanite thing to do. It is still warm and sunny in the beer garden, and so as he stands, he slips on a pair of sunglasses. Earlier, he had admitted that he has difficulty wearing sunglasses in Manchester, suggestive, as they can be to others, of someone who has developed ideas above their station.

"The last time I put them on here I was with my sister," he'd said. "She stopped in her tracks, laughed, and told me to take them off straight away."

Recalling this now, he swiftly removes them before anyone sees him, and replaces them back in his pocket. He goes home squinting into the sun. His sister would be proud.

'Build a Rocket Boys!' is available now on Fiction. Elbow play Glastonbury on 25 June