Assuming you prefer not to remortgage the house in order to buy a ticket for Barbra Streisand’s next farewell tour, a soirée with Steven Brinberg is definitely the next best thing. Yes, I can already hear your objections: isn’t there something just a little too, well, camp about the idea of a man impersonating the world’s most precious diva?

Well, in normal circumstances, that would be true. Camp too often becomes an excuse for woefully untalented acts to pretend that they are the funniest thing since La Cage Aux Folles. (Yes, I mean you, Kiki & Herb.) But the New Yorker Steven Brinberg understands that while it’s easy to send up La Streisand’s foibles, making her seem human (or at least almost human) and getting the voice right is no mean feat.

Having seen him before, in the much smaller surroundings of the Jermyn Street Theatre, I wondered whether the joke would still seem fresh several years later. The answer is an emphatic yes. The faded glamour of Too2Much — which occupies the former premises of the Raymond Revue Bar — is well suited to the louche, cocktail-hour mood of the show. (Any upright reader of The Times who can make it past the Soho fleshpot attractions and through the door without looking furtive surely deserves a year’s free subscription.)

Accompanied by the pianist Nathan Martin, Brinberg eschews Grand Guignol and focuses on the tiny gestures — the delicate flutter of a hand, the faux-humble sighs — that are an essential part of the superstar’s armoury. This is a woman who suffers private-jet-lag when she flies the Atlantic. And while it’s fair to say that no one could capture Streisand’s arena-bursting vocals at full blast, Brinberg offers an uncannily accurate version of her low-key ballads. The jokes are wonderfully understated, and even though Streisand’s husband, James Brolin, once again comes in for constant mockery, there is a constant undertow of affection. In a funny sort of way, Brinberg is the best press agent Streisand has ever had.

Continues Wednesday to Saturday. The Lowry, Salford Quays, Sept 18, and Norwich Playhouse, Sept 26