It’s an impressive record: Richard O’Brien created The Rocky Horror Show in 1973, and it’s since become a money-spinning phenomenon like no other, even acquiring a dress code for audience members. Among forbidden items of clothing are “sandals, anoraks, or anything connected with the acquisition of British Rail rolling stock numbers”.

Now O’Brien, director Bob Carlton (best known for Return to the Forbidden Planet), and composer Richard Hartley (who scored Rocky Horror) have changed direction. The Stripper is set in Pine City, California, in 1961. Lieutenant Al Wheeler is investigating the death of Patty, who’s fallen from a 15th- floor window. Wheeler’s enquiries lead him to Patty’s cousin, Deadpan Dolores, who strips — there’s one brief flash of flesh — at the Blue Extravaganza, the sort of dump where half the light bulbs don’t work (Rodney Ford’s set design is very clever). “What have I done wrong, Loo-tenant?” drawls blond Dolores, “Is a bit of bumping and grinding wrong?”

It soon becomes apparent that O’Brien (who wrote the lyrics) has latched on to the twin worlds of pulp fiction, and the current obsession with police procedurals. He sends up both worlds very nicely — when, for instance, did you see a cadaver examination on Channel 5’s CSI being followed by a soft shoe shuffle, executed by a pathologist wearing an improbable wig?

The star part gets a star performance: Jonathan Wrather expertly portrays a Lieutenant Wheeler who has real depth of character. Yes, he’s testosterone-fuelled, and doesn’t always think of the possible consequences of hopping into bed with someone who might later be implicated in his investigations. But underneath is a decent cop, determined to get at the truth. Following close behind in star quality is Jack Edwards, playing a gay florist, who has — this being 1961 America — to assure the lieutenant that he has bedded many a girl himself. His big number, I Confess, is the highlight of the entire show, but the whole score, superbly played by an on-stage band, is beautifully crafted to reflect the early 1960s’ easy listening music scene.

Emma-Jayne Appleyard, playing Dolores, also sings strongly, and a uniformly excellent cast includes O’Brien himself, playing the owner of a dodgy dating agency.

Is The Stripper going to become an iconic show like Rocky Horror? It’s not in the same league yet — even allowing for some first-night technical glitches, the show needs speeding up, and more unadulterated pzazz. But there’s excellent material here, which could very much stand the test of time.

Until Saturday. Tickets 0844 871 7652 or (www.ambassadortickets.com/miltonkeynes).