As wartime bombs fall on London, deep underground alongside Piccadilly Circus a radio programme called Variety Bandwagon is about to go on the air. But all is not well in the subterranean surroundings of the Criterion Theatre, which has become a BBC studio for the duration. The star, Sammy Shaw, has vanished, and so has the ventriloquist. The BBC producer, imposingly named Heathcliffe Bultitude, is not amused.

Thus begins the musical Radio Times. Conceived by Alex Armitage, and featuring music by Noel Gay (his grandfather), the show premiered in 1992. Now it’s been given a sparkling new production by the Watermill, with Caroline Leslie as director, and musical arrangements from Paul Herbert.

A big name has been brought in to play Shaw: Gary Wilmot (above), used to filling the biggest theatres in the land, adapts effortlessly (or so it seems) to the intimate Watermill as he works his way through his numbers, and a script stuffed with double entendres — Sammy is also Variety Bandwagon’s resident comic. There is a slight problem though: Wilmot radiates such warmth and bonhomie that it’s difficult to believe Shaw has behaved in a “pig-headed and insensitive manner” (his words) towards his wife Olive (Anna-Jane Casey), or that he’s a bit too interested in fellow singer Amy (Vivien Carter).

Peachy supporting roles, eagerly seized, go to Julian Littman as Wilf, the cynical warm-up man, and Christian Edwards, who plays Jeeps, the BBC sound effects operator. But peachiest of all is the role of Bultitude, the producer. At first appearing to be a pompous, rulebook-quoting BBC functionary, Bultitude has many hidden and totally unexpected talents, and Andrew C Wadsworth (below) makes a wonderful job of the part.

But the real purpose of Radio Times is to give an airing to 21 evergreen Noel Gay numbers, You’ve Done Something to My Heart, and Run Rabbit Run among them. All are delivered with tremendous verve and precision by principal and ensemble cast members alike, often to Alistair David’s hilarious choreography — Hey Little Hen and Ali Baba’s Camel in particular are a side-splitting wonder to behold. Some punchlines were mumbled into obscurity on press night, but that’ll soon be sorted. The Watermill has once again produced a really first-rate musical, and has timed it right as well: this show is a great pick-me-up in this depressing era.

Until September 24. Tickets: www.watermill.org.uk or 01635 46044.