Imelda May, Liquid Room, Edinburgh

When it comes to the Seven Ages of popular music we are now well into the post-retro era. In 2011 every artist is a magpie and every song sails out beneath a pirate flag, greedily plundering where it pleases. When everything that has gone before is up for grabs, it’s now simply a question of how you want your yesterdays delivered: rare, medium or well done?

Imelda May might reheat the past but at least she serves it up red hot. A performer since her early teens, her career has crept forward by increments. Now in her mid-thirties, May's third album Mayhem, released late last year, has provided her with a commercial breakthrough, breaching the UK Top 10 and giving her a taste of mainstream exposure. Last night she looked born to it.

May made much more sense live than on record, partly because she so completely looked the part. Sewn into a pencil dress, her pale face slashed with red lippy and her trademark vanilla pin-curl jutting out from her scraped-back black hair, she seemed every inch the drive-in vamp of countless Fifties films. Throw in the kind of wonderfully abrasive Dublin accent you could file your nails on and, well, she’s never going to struggle to hold an audience's attention, especially in a relatively small club like the Liquid Room.

Indeed, she seems already to have attracted a devoted following. Half the crowd last night appeared to consist of girls who wanted to look like her – firmly answering the question: to beehive or not to beehive? - while the other half seemed to be Irish. Even if she had stuttered she could hardly have failed; as it was, she was blazing from the get-go.

Most of the set was pulled from Mayhem and displayed a surprising diversity (she even gave us two versions of her latest single “Inside Out”: one cooked slow in a sultry New Orleans style; the other pure retro-pop). May’s sound ranges over early rockabilly, Sun-era rock’n’roll, jazz-tinged torch song, blues, country and Fifties pop, but she stamped and stomped her personality all over the past in a way that instantly dispelled any notions of pastiche.

What matters most about May, way before the Ann-Margret stylings and cute kiss-curl, is that she is a phenomenal rock'n'roll singer: she gave primetime Wanda Jackson a run for her money on the full-throated holler of “Eternity” and “Johnny Got a Boom Boom”, but she also summoned up the sweet, quiet ache of Patsy Cline on the slow border-country of “I’m Alive”. There was a touch of Amy Winehouse sass in her more jazzy moments, and when things got really wild during the surf-punk “Psycho” there was even a hint of the chippy, confrontational attitude of late-Seventies pioneers like The Slits and X-Ray Spex.

It helped that her band were superb, tight and razor-sharp. In white trousers and spats, her guitarist – and husband – Darrel Higham looked for all the world like David Morrissey auditioning for a remake of Miller's Crossing. Al Page was sensational on stand-up bass, while Steve Rushton on drums and Dave Priseman on trumpet and guitar completed a sterling five-piece line-up.

They visited Howlin’ Wolf on the spare, stalking blues of “Poor Boy” and unleashed an utterly ferocious version of Johnny Burnette’s rockabilly riot “The Train Kept Rollin’”, which might just have been the most enjoyable sound I've heard barrelling from a stage so far this year. Elsewhere there were nods to Link Wray in “Psycho”, while the snaking rumba of “Big Bad Handsome Man” had a little of Tom Waits's loose-limbed swagger.

May worked the crowd like an old hand. On the low and lustful “All For You” she wiggled and wooed like a cross between Marilyn Monroe and Carmen Miranda, dissolving into giggles when it all threatened to get too steamy. On the gospel-tinged “Proud and Humble” she engaged in a fabulous a capella call and response with a punter 20 rows back who seemed to have borrowed Tom Jones’s larynx for the night. During the encore the pair sparred again on May’s jived-up version of “Tainted Love”.

That sense of fun and generosity seemed to sum up the spirit of this music. It’s hard to see May's fiendishly enjoyable rock'n'roll ever selling in the multimillions or filling arenas, but she was clearly born to kick up the dust in the kind of places where you can throw a tennis ball from the stage and hit the back of the room. On last night’s sizzling evidence, May has the chops and chutzpah to command - and thrill - a live audience for as long as she wishes to do so.

• Find Mayhem on Amazon
• Imelda May is touring the UK until 19 February

Watch Imelda May perform "Mayhem" on Later... Live with Jools Holland