If it seemed odd that a Mercury prize nominee was playing a free show in the foyer of the Queen Elizabeth Hall in front of perhaps 150 people – some committed, but many merely curious – it had to be remembered that until the Mercury nod, Speech Debelle was unknown outside London's hip hop scene. It's impossible to predict whether the publicity boost will usher her toward the success that has eluded most British female rappers, but by the end of this enjoyable show, most of the audience must have been crossing their fingers for her.

Debelle's band, the Therapists (named after her debut album, Speech Therapy), created an organic, jazz-influenced groove that did much more for her small voice than the usual hip-hop beats and electronics would have. Dressed down in glasses, T-shirt and leggings, she went with the relaxed flow, making graceful arcs with her hands and delivering her wordy rhymes with half-shut eyes. This was music so slinky and cool it should have come with a Left Bank café attached – all the more so when 2003 Mercury nominee Soweto Kinch arrived to contribute silky saxophone to the last number, Buddy Love. (Was that the sax riff from Careless Whisper that he was playing, by the way? It certainly sounded like it.)

Debelle wasn't quite as laidback as this makes her sound, though; there is real hard-knock experience in her lyrics. Where she might have started the show with a party tune, she chose instead Searching, a song about her stints of homelessness. There was also Go Then, Bye, which likens a romantic break-up to an asthma attack ("and I don't even smoke"), and in the tongue-twisting tour de force The Key, she frets about "negativity" and the uphill task of changing people's attitudes.

Debelle probably isn't voguish enough to win next month, but her fresh new voice makes her a very welcome presence in pop.

At Bestival, Isle of Wight on 13 September. Details: www.bestival.net