It came billed as "... and the Vandellas", but there is no vocal backup for Martha Reeves in Edinburgh, just a locally sourced eight-piece band. The septuagenarian Tamla Motown queen does not mention the lack of soul sisters, although she covers almost every other topic under the sun with a breathless, gossipy commentary that fills every gap between solid recreations of her timeless hits.

This is the first of two sold-out nights at the fringe, and the "anything goes" mentality of the world's biggest arts festival seems to be infectious. On the upbeat stalker anthem Nowhere to Run, audience participation is warmly encouraged, and by the time Reeves gets to Jimmy Mack, she has targeted specific punters to sing the chorus as if auditioning for replacement Vandellas. A young chap in a Spider-Man T-shirt does particularly well.

After more than 50 years in the game, Reeves could most likely perform a slick revue in her sleep. Occasional sound issues mean this gig is more of an appreciation than a revelation, but it goes memorably off-piste when one fan makes a special plea for Uniform, a sexy come-on from Reeves's 2004 solo album Home to You. She is treated to a burst of spine-tingling a cappella.

As the inevitable finale rolls round, Reeves lists all the artists who have covered Dancing in the Street – an impressive roll call of talent, although among the various creaky rock icons, it is Dusty Springfield who gets the biggest cheer. Amid her beloved Detroit's bankruptcy and mass foreclosures, Reeves stakes a claim of immutable ownership: "This is my song."

Her signature hit is robust enough to sustain cheeky additional grafts of Signed, Sealed, Delivered I'm Yours and Knock on Wood on to its midsection. And with nowhere else for the show to go, Reeves strong-arms her band into playing Dancing in the Street all over again, inviting the crowd on stage and leading them step-by-step through the Funky Chicken. "Now dance like James Brown!" she yells. Like Reeves herself, it's quite something.