Speech Debelle, Scala, London

Look at you all!" says Speech Debelle, admiring a fairly full house of mostly well-heeled white pseudo-bohemians. "See what the Mercury can do!"

This is the 23-year-old south Londoner's first big hometown gig since her Mercury Prize win last month with her debut album, Speech Therapy. The insupportable implication that it's 2009's best British LP has made some think the Mercury has lost its way, but don't blame that on Speech. Post-prize questions about exactly how rough she was living during the three no-fixed-abode years that informed Speech Therapy don't damage her artistic authenticity, either.

Her support act, Kasha, rests himself on such shifting sands when he insists a rap is "a true story ... if you have a heart you will be touched." Actually, there are no moments in his set or Debelle's that put such hurt over, and Debelle doesn't even try. These days, she is having the authentic time of her life, her girlish voice bubbling with joy.

The trio backing her – double-bass, acoustic guitar and drums – emphasise this isn't hip-hop, but rapped jazz. Race doesn't define her, either, when Glasvegas's white working-class Scot James Allan articulates themes of absconding fathers and destructive violence with greater force. You might compare her to Dizzee Rascal. But only in the way he has used early trials not as weights to hobble his art, but fuel for new experience. In that spirit, Debelle shouts "this one goes out to all my people with ambition" during "Finish This Album". "I'm gonna represent the youth ... eat more fruit," she adds, wisely undercutting any spokeswoman for a generation aspirations. She'll fix the world when she can stay out of the fridge.

Debelle already looks grateful for her homeless years, and has lost interest in "Daddy's Little Girl", her most furiously vengeful song to the past. "Searching" begins "2am in my hostel bed", but it is delivered with the ebullience of someone far from there. She hurls herself hardest into "Go Then Bye", a pop song about a love affair's ordinary end.

Court cases are for the men in her songs, half-wanted babies for the girls. But Debelle's biggest problem is "having to look good all day now". The paparazzi and many Mercury-drawn fans may soon leave her performance-poet jazz to its natural tiny constituency. But Debelle the woman remains a winner.