Elbow, Brighton Dome

Garvey's thank you to his patient followers

"You need forgiveness when you've been in a band this long," says Elbow's Guy Garvey, squinting into the lights. Forgiveness for what, you wonder? For keeping the dream alive in the face of intolerable bad luck? For staying together when most criminally under-appreciated quintets would have gone their separate ways and retrained as IT operators?

Elbow don't need forgiveness, they need a medal. Which, by some curious twist of fate, is exactly what they've got after almost 20 years of service – first a Mercury Prize and now a Brit. It's an extraordinary turn of events in a fickle industry that rarely rewards perseverance.

And with recognition has come a hint of confidence. Where Garvey once maintained a nervous silence in between songs, he now shares confessional stories and bats away the comments of over-zealous hecklers ("I can't give you a hug, man. I'm busy"). Sure, as the front man of an unexpectedly mainstream indie-rock band, the bearded, paunchy, thirtysomething Garvey cuts an unlikely figure. The number of times he unbuttons, buttons up, takes off and then puts on his suit jacket suggests a man not entirely at ease with his physical self. But it's this seam of vulnerability, combined with his sweet affability, that makes him one of the most impassioned singers around. It's a shame that the band habitually mentioned in the same breath as Elbow is Coldplay, because neither Chris Martin nor his quivering whine are a patch on Garvey's innate humanity and charisma.

The show is an emotional one for artist and audience, with clear disbelief and euphoria on both sides that Elbow have finally come out on top. For want of a better cliché, there's a lot of love in the room, a fact not lost on Garvey who delivers repeated and heartfelt thanks to the crowd for getting him where he is today.

The set draws heavily on Elbow's much-feted album The Seldom Seen Kid, though the band's choice of older numbers – from the woozy, psychedelic "Any Day Now" and the exquisitely gruelling love song "Newborn" – reveals them for the multi-textured, wide-reaching and quietly ambitious band that they are.

Experience counts for a lot and two decades of trawling the live circuit means Elbow know how to pace a show to perfection. Giant crescendos are followed by quieter episodes which lull the crowd into an introspective daze. For "Weather To Fly" the band huddle together for an acoustic intro (though not before necking some shots for a mid-set pick-me-up). In contrast, "Starlings" with its sudden stabs of brass, brims with wayward melodrama while the stomping, swelling "Grounds For Divorce" is quite simply thrilling.

Finally comes the life-affirming "One Day Like This" with its repeated refrain "Throw those curtains wide/One day like this a year would see me right". It's undoubtedly a classic, eloquently articulating the purity of happiness, and made all the more poignant by the band's sudden change in fortune.

But – and I'm splitting hairs here – it's also the kind of song that those masters of manipulation Coldplay have made a career out of. You can only assume that Elbow's emotional integrity will prevail and they will resist the urge to write too many more like it. In the age of preening, middle-of-the-road indie bands, we need them now more than ever.