Dawn Kinnard, Bar Academy, London

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There's a story behind the whisky-soaked, lived-in voice that belongs to Dawn Kinnard. The daughter of a Baptist preacher in Pennsylvania, Kinnard would take her guitar to her hairdressing job, where she started to write songs; she sold her treasured Harley-Davidson to record her mini-album. That she was discovered singing in a Nashville bar is fitting, given her smoky blues and country sound.

Less fitting, however, is the Islington Bar Academy. A long venue with a bar in the centre best suited to noisy indie rock bands is trouble for a solo artist. With just her acoustic guitar and a keyboardist, she requires the intimacy of a hushed and reverent audience to immerse the listener in her woozy stories of addiction, love, freedom and paranoia.

Constant audible talking can certainly be blamed for her missing the occasional cue, and almost stops her from singing "White Walls", one of the best tracks from her recent debut album, The Courtesy Fall. "The next one is a ballad about a friend of mine who is drug-addicted, but I'm not going to play that one with how loud it is," she says soberly. But perform it she does, its vulnerable wispy vocals against light guitar strumming and piano emotive and compelling in their earthy honesty.

In the short time Kinnard has been on the scene she has performed on Later... with Jools Holland; next month she headlines Bush Hall; and tonight she features top of the bill at Time Out's "On the Up", which showcases music's rising stars. Belying the Dusty Springfield comparisons (for her husky voice and sculpted blond hair), she glides between slow, sleazy, jazzy cabaret-style songs such as "Fortune Teller", and the more captivating piano rock of "You Are My Kite" and "All In Your Head". Her voice is reminiscent of the Welsh star Cerys Matthews, who features on her album, but never lifts above a certain pitch and volume. Her songs can be instantly accessible, in a Norah Jones-meets-Coldplay sort of way, but a song like the confrontational "Devil's Flame" turns this image on its head. So does the perverse interlude in which she reads out a poem – a misjudged moment. Gospel is an unusual encore, too.

But there remains the undoubted sense, when you have been reeled in by her soul-baring songs, that the memorable melodies will haunt you for days.