The walls of the Sinners Club are covered in photos. Ruth Ellis looks out of them in black and white, platinum blonde with big, beautiful eyes. She looks a different woman in every picture. In one, she's in stockings and suspenders, one leg cocked up on a chair, eyeing the camera seductively. In another, she smiles out like Marilyn Monroe. Sometimes she looks like a society belle, at others a sweetheart, and elsewhere a call girl. She was all and none of the above.

Ellis was the last woman to be executed in Great Britain. She went to the gallows on 13 July 1955, convicted of murdering her lover David Blakely. For a while beforehand, though, she was the scourge of the tabloid press: her death sentence splashed across the front pages, 'RUTH ELLIS TO HANG'; her face staring out below. No wonder; Ellis' story had all the salaciousness and shock factor to shift papers back then (and now, for that matter). An ex-escort with movie star looks who murders her man? Catnip on Fleet Street.

Sinners Club doesn't exonerate her exactly, but it does offer reappraisal. Ellis accepted her fate. "An eye for an eye," she told reporters; one death deserves another. But her crime sprang from the very same principle. For years, Blakely had beaten her, cheated on her and sexually abused one of her daughters. Ellis mightn't be quite the woman she was paraded as.

Gagglebabble's intimate cabaret musical – an immersive gig, if you prefer – rattles through Ellis' life in a rather abstract way. Rather than biographical timeline, Lucy Rivers' songs explore aspects of her character. We're privy to a live concept album recording, where Rivers and her band The Bad Mothers are overseen by an overbearing unseen producer, a mic'd up voice and an eye on proceedings, who keeps overriding and belittling his female star.

Instead of clear narrative, meaning mostly comes through tone. Rivers' songs are shot through with sounds of Americana, turning a tawdry gutter press tale into something more swaggering: proper old pulp fiction. Sinners Club lifts Ellis out of one tradition and into another, transforming the Soho slapper of the red-tops into some kind of glam, freewheeling outlaw – Bonnie minus Clyde, a rebel without a cause. It almost celebrates her as a sexual revolutionary – the woman who took the fight back to the patriarchy – though Rivers never entirely absolves her or lets her off the hook.

As bio-musicals go, it's not dissimilar to Neon Neon's Praxis Makes Perfect – smart politics set to pop – and one or two of Rivers songs are real stadium pleasers, all the more potent squeezed into the back room of a pub for Titas Halder's production. Rivers is riveting too: cracked and fabulous, wry and ferocious. She sings a peach of a bruised love song and blasts out a howl of vengeful emotion. A woman's place is in the Sinners Club.

Sinners Club runs at The Other Room in Cardiff until 24 February, then transfers to Theatre Clwyd, Mold 2 to 18 March.