Whodunnit? Forger Hilary Clinton, cat burglar Zayn Malik or sleazy Arsene Wenger

If Raymond Chandler had fallen into uneasy dreams over a copy of Heat Magazine he might have seen something like Murder in Successville.

If, as Andy Warhol prophesised, everyone will be famous in the future, the town of Successville is way ahead of its time. Populated with celebrity impersonators, the show blithely assigns familiar faces to the myriad roles of a detective plot. Gordon Ramsay, for instance, is the implacable police Chief, Lana Del Rey sometimes appears as its dreamy pathologist, Alan Carr and a frighteningly mute Jimmy Carr made an early impression as mobster brothers.

Each week, a genuine celebrity is invited in to help solve a murder, through an improvised investigation led by the star, DI Sleet (Tom Davis), a bearishly big man with a much nimbler wit.

Murder in Successville is the kind of show that could only exist as we approach an infinite number of TV channels; an unlikely and daftly entertaining bit of programming that stretches all theories of probability. Returning for its third series, it begins by assigning Sleet his mirror image, the presenter Richard Osman, another quick-witted giant, to solve the murder of a visual artist. “Bing bong,” she says, shortly before harm befalls her. “I’m Björk, the sparkling pixie dream child.” They really do their homework.

Celebrity impressions are otherwise goofily imperfect in Successville, somewhere on a scale between Bo' Selecta! and Rob Bryden, more like indications often made cartoonish with prosthetics. The suspects this week are forger-turned-teacher, Hilary Clinton (“Nobody plays by the rules anymore!”), neurotic cat burglar Zayn Malik and sleazy avant-garde gallery owner Arsene Wenger. The real joy of the show, though, is its mad, immersive, improvisational game. Going undercover as a live model and an art student, the “Yes, and…” steps of Sleet and Osman’s escalating improv rise to an hysterical crescendo. “Come hither and blow upon my penis,” Sleet inveigles his partner. “But make it look normal.”

As Sleet, Collins is beginning to play fast and loose with the pleasingly hokey form, brushing aside a rarely glimpsed camera man, and, in a later episode, complaining about the show’s production values when given truth serum. With the right partner, his wild freewheeling is a contagious joy, and Osman, game for anything, is the right partner. “You pick up on every little detail,” Sleet remonstrates, an odd complaint when that is the point of the show, slipping clues into the jazz of its jokes and celebrity cackle.

That Osman solves the murder is no mystery; within Successville’s dizzy take on popular culture, the real mystery is how we are able to concentrate on anything any more.