The Pipettes, King's College, London

The Pipettes are a band whose time has arrived. It's been a long time coming. The first time I saw the Brighton girl trio through the alcohol haze of New Year's Eve 2003, supporting British Sea Power, it wasn't entirely clear whether they were for real, or simply a bunch of mates having a laugh. On subsequent, more sober viewing, it became blindingly obvious that this was the real deal.

They had the songs: joyously witty, infectiously memorable tunes in the tradition of Phil Spector, Tamla Motown and the Brill Building. They had the look: specially-made matching polka dot dresses and a backing band called The Cassettes who, in their monogrammed knitwear, could pass for frat boy extras in the Happy Days café. Most of all, they had the charm: hand-jive moves from heaven, and audacious claims that "we're the prettiest girls you've ever met". At every gig, they slapped huge grins on everyone's faces. The whole world, surely, was about to fall in love with The Pipettes.

Somehow, it didn't happen. For two frustrating years, Pipettes fans watched as they worked the circuit, playing support acts with no sign of the big breakthrough.

Things started to turn around when they were picked up by commendably eclectic indie label Memphis Industries. A run of single releases followed, and tonight's show is the launch party for the latest one, "Pull Shapes" (accompanied by an absolutely brilliant video, re-editing Russ Meyer's cult classic Beyond The Valley of The Dolls), with their debut album, We Are The Pipettes, due out the week after next.

It's a good time to be catching up with Rosé, Riotbecki (the one with the knowingly nerdy specs) and new-ish member Gwenno, who has a parallel solo career as Gwenno Saunders, a Welsh Music Award winner who sings in Cymraeg and Cornish. It's she, in her Welsh accent, who says, "This is lllovely, inni?" Her glee is understandable. This is the first time The Pipettes have headlined this kind of venue, to this kind of crowd - several lookalikes (which is always a good sign), much enthusiastic overhead handclapping - and seen that, finally, the snowball is rolling.

Perhaps the world has realised that there's more to these girls than mere period pastiche. Sure, they've got all the moves: there's the stop-in-the-name-of-love and the streetcorner finger-click. They've got the musical signatures: the authentic Sixties rallentandos before the chorus, an actual "Be My Baby" drumbeat and the conciseness (the longest song on the album lasts an epic three minutes and three seconds). Suffice to say that a little panache goes a long way and every sha-la-la-la and every whoah-oh-oh still shines. There's also just the right amount of amateurishness to what they do: cracking each other up, looking like they're having the best fun in the world. If I was a girl, I'd want to be a Pipette.

Furthermore, there's something inescapably contemporary about The Pipettes. They belong in a world where the Vietnam War is over and mobile phones exist. Their Sixties forebears were mostly sweet and innocent. The Pipettes are knowing, in the way Debbie Harry was knowing. They have songs called "Your Kisses Are Wasted On Me", "Why Did You Stay?" and "One Night Stand", and an exchange that goes, "But he was so sweet!/ Well, I've had just about enough of sweet..." The Pipettes are, essentially, the anti-Shirelles: they don't care if you still love them tomorrow.

It's telling that the sole exception, "I Love You" ("There will never be a time when we have to say goodbye"), is their weakest, wettest moment. That said, the dreamy ballad "Tell Me What You Want" could be early Saint Etienne (no higher compliment). Right now, The Pipettes are looking like the best self-made British girl group since Kenickie. They're on the brink. Now make them stars.

s.price@independent.co.uk