Martha Wainwright, Royal Festival Hall, London

Martha breaks free of family shackles to reveal her own voice

Of the many singing Wainwrights, Martha is the one with the voice.

She seemed modest and unsure of her place in such an intimidating clan at first. But her new album, I Know You're Married But I've Got Feelings Too, is as slyly cocky and carnal as its title. Sharing KT Tunstall's producer, it could vault her past brother Rufus's stardom. But, introducing its songs to London last night, open-hearted art drives her more than ambition.

High-heeled leather boots, short skirt and tight top are Wainwright's outfit for the night, and her legs brace to as if to leap forward. With her strong, supple, deep voice, she is inviting, yet ferally fierce. Without apparently trying to, she toys with her straight female sexuality, as much as gay male Rufus does his.

The prim venue proves mausoleum-quiet at first. "It makes me nervous," she says. "Jesus and Mary" wakes us up. Powered by her rock holler, it is a cinematic tour through emotionally and physically scarring terrain. "I have lost so many friends," she sings later. "I have made so many memories" – a transaction which, hungry for life as she seems, doesn't phase her. This inclusive spirit means Ed Harcourt and The Magic Numbers' Romeo Stoddart are invited on, to play their own songs. But Wainwright's bellowing harmonies capsize their contributions.

For all her band's pop fullness, it is solo with acoustic guitar where she is loosest and fiercest – as on "Tower", her quaintly termed "topical song" about 9/11 and the war. "Rebuild the tower, make it last longer...stronger," she sings, with sensuality which softly seduces you closer, to hear, disarmed, its end: "Give up your power."

"In my filthy, dirty dreams," Wainwright claims, "there are men singing my songs." Beth Orton comes on instead, to duet on Syd Barrett's "See Emily Play". Then "Jimi" turns love and sex into punchily melodic, globe-trotting adventure. "I'm scared to death, of what you've become," she claims next. But, as she smiles at the sound of another sleekly purring pop song, such worries seem in the past.

"Made it to the moon," she exhales, in her newly excited, confident mood.

It is when she goes solo again that she fascinates most, as if her new pop songs cloak something still more raw and thrilling. "Do you know how it feels, to be on your own, in your own home?" she enquires, quoting Dylan and excoriating her father, Loudon Wainwright III, on "Bloody Mother Fucking Asshole". Singing it has surely softened even this old pain. She concludes with a quavering, unhinged French chanson. Martha has her own voice now.