Martha Wainwright, Shepherds Bush Empire, London

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This February, Martha Wainwright was playing at the Barfly, delivering a loose set interspersed with shots of bourbon and lengthy chats with the audience. She was back with a band a month or so later when her excellent debut album was first released on indie label Drowned in Sound, supporting Wilco and working some of the nation's hardier music venues. This headlining concert in Shepherd's Bush is an arrival of sorts, into a bigger kind of league.

The shots of bourbon may have gone, at least from the front of the stage, but the between-song patter would suit Mae West, and Wainwright plays virtually the whole of her album over the next couple of hours or so. She's got a Canadian dry humour when dealing with the sexual life, and her songs have it, but there's a lot of broken emotional fabric in them too. They are filled with great lines - "I've been seen crossing someone else's mind", "there are no hats, gloves, scarves for the heart"- and their delivery can hush a full house with an emotional intensity leavened by dryness, wit and lyrical detail, and the superb qualities of the voice.

Wainwright hits the stage in a little black dress and stilettos, a kind of alt-country vamp with a guitar and a sharp eye for how men do things; she'll have plenty of observational experience of that just within the family, via dad Loudon and brother Rufus. Her cousin Lily Lanken helps with the beautiful harmony vocals that are a strong feature of the album, and the four-piece band comprising keyboards, guitar, bass and drums, are a crack unit, to be sure, not a foot wrong, not a hair out of place.

The guitar slides and sways as good as any Southern breeze, the notes bending like the tops of palm trees in some luxurious mirage, but their full and perfectly formed band sound envelops Wainwright's strong, highly individual material perhaps a little too closely in its grip.

Wainwright opens with one of the album's highlights, the powerful "Factory", and goes on to deliver incisive versions of the lost-love song "Ball and Chain", the seductive "When The Day is Short", and the great rolling litanies of "The Maker". Then the band slips away for a central section of solo performances that instantly seem to lose several layers of vinyl silk, bringing out the sharp contours of her material alongside some superb covers, featuring duos and trios with different band members.

The covers can be read as personal selections from an artist well-versed in the canon. Strumming strange tunings at a rhythm like a worrying heartbeat, she twists a brilliant alternative reading from the Stones' "Street Fighting Man", and there's a breathtaking version of Cohen's "Tower of Song", as well as a warmly received duet with Teddy Thompson (another heir apparent to a daunting family tradition), and in "Nobody Knows You When You're Down and Out", she reprises the brilliant vaudeville turn she did for her "other mum" Linda Thompson's Strange How Potent music hall night in the summer.

But the voice says it all, more or less, an instrument both malleable and arrestingly powerful, a voice with rips and tears in it, a place where you can feel the depths of things. Sometimes it breaks like the saddest thing in the world, and sometimes it blows like one of the hardest. But it retains a dryness that eludes the kinds of singers you might hear mentioned in the same breath - fellow Canadian Alanis Morissette, for example. It's a blues holler that's earned its keep. Wainwright comes with quite a lot of back-story, but there's a great deal more to come. This story's got legs.