"It's not a good look, a guy playing with a girl," reckons Jamie Hince, a few songs into The Kills' set at Heaven. But it's actually a great look, when the girl looks as great as Alison Mosshart. Hair like a bird's nest recently ransacked by angry chicks, wire-thin frame poured into op-art top, black leggings and white miniskirt that she keeps tugging at, Amy Winehouse style – Mosshart is her era's defining "rock chick", the Janis Joplin or Debbie Harry of our time. All that's needed are a few bona fide hits, and the duo's new album, Blood Pressures, should provide them.
They're one of those acts who really come into their own on stage, however. Tonight's set opens with the galloping drum-machine of "No Wow", Hince's damped guitar vamp punctuated with occasional jagged bursts of serrated noise flourishes, to each of which Mosshart spasms as if electrocuted, wired directly into some rock'n'roll mains. Though often compared to The White Stripes, the pulse and attitude is more akin to that of pioneering electro-rockers Suicide, yoking primal rock swagger to minimal noise riffs, such as the angular simplicity of "Future Starts Slow", in which Mosshart invites us to "go in search of my right mind", with the delinquent panache of one confident that no such thing exists.
The raggedy blues stomp of "Fried My Little Brains" and the cyclical arpeggios of the bluesy "Kissy Kissy", both from the duo's 2003 debut, Keep on Your Mean Side, suggest that rather than Jack White, the core influence on the band's sound is actually the Jon Spencer Blues Explosion, whose central role in revitalising blues and rockabilly as minimalist new-wave rock has been overlooked in recent years. But sparseness is the crucial element in The Kills' sound: as soon as either Hince or Mosshart wanders over to the keyboard at the rear, for "Baby Says" and "The Last Goodbye", there's a palpable dip in excitement, even though their piano lines are no more decorous or complex than their guitar riffs.
What's most impressive about the show, though, is that the new material – the loping grunge polka of "Satellite", the hypnotic, room-shaking throb of "DNA", and the implacable stomp of "The Heart Is a Beating Drum" – provides the most infectious moments of their set, suggesting that The Kills are developing in a direction that could yet find them in a head-on collision with the mainstream. Not that they're ever likely to lose the outlaw charm that is their essential appeal: when Alison Mosshart sings "I am a fever, I ain't born typical", she's simply stating the obvious.