Our Man in Havana review – Graham Greene novel becomes a witty and suspenseful musical

Graham Greene drew on his own experience in MI6 for his darkly comic 1958 novel. It was so successful that Carol Reed's film starring Alec Guinness followed swiftly in 1959. Set in pre-Castro Cuba, when the island's capital had a well-earned reputation as a hot destination – and not just because of the weather – the novel is a satire sending up the Cold War machinations of Britain's secret service from the inside. Uncannily, it also seems to succeed in predicting the ‘Cuban missile crisis', when the world was at its nearest yet to nuclear war, thanks to Fidel Castro's revolutionary government providing a base from which Russian nuclear missiles might be launched.

Now, as a new global crisis threatens, can a musical based on Greene's prescient tale find its moment? The answer is a resounding ‘yes'. Richard Hough's witty book and lyrics and Ben Morales Frost's music conjure up a real period feel and the exotic gaiety of the island playground of the rich and famous (Sinatra holidayed there while Eartha Kitt and many more big international stars appeared in cabaret in the island's casinos). Their six-strong cast, under the nimble direction of Abigail Pickard Price, serve the show and its creators wonderfully well, switching instruments and characters with equal aplomb, to tell a story as suspenseful as it is drily comic.

Nigel Lister is pitch perfect as Greene's antihero James Wormold, a vacuum-cleaner salesman down on his uppers, and a single dad valiantly striving not just to support his ebulliently aspirational 17-year old daughter Milly, but to satisfy her every whim – currently to have her own racehorse. So when MI6 recruiter Hawthorne plies him with the heady spirits he craves (and collects in miniature take-home bottles too) in a local bar that's open all hours, it's a done deal.

Lister finds exactly the period feel of the man, in both looks and delivery, his lugubrious wit and resourcefulness as he hits on the dangerous idea of inventing contacts and leads, using real names he finds in the local papers. He's nimble-fingered on the piano keys too. Daniella Agredo Piper makes for a deliciously exuberant Milly, twisting her dad round her little finger and playing the sax with the same insouciance. And Alvaro Flores is equally convincing as the deviously insistent Hawthorne; and later, Segura, the scary local military leader with dictatorial ambitions and a moustache to match – plus a worrying desire to marry the much younger Milly.

Will Wormold keep Segura at bay and get Milly to agree to leave the island before it's too late as his inventions prove to have an uncanny way of proving to be dangerously real? As he tries to keep all the balls in the air, he is grateful to his one real friend in need and confidant Dr Hasselbacher (sympathetic Adam Keast).
An extra curveball comes when the feisty Beatrice turns up on the island declaring she has been sent by MI6 HQ to provide secretarial support. Paula James' support is welcomed by the audience at least, even if Wormold has his suspicions, for we have seen this lovely mover and thrilled to her huge voice as the sultry Maria singing and dancing up a storm on the floor in the bar.

It's down to a terrific team – onstage MD Antonio Sanchez, movement director Andrea Pelaez and associate choreographer Chris Cuming – that the music and action are seamless on designer Kat Heath's extraordinarily versatile set. The breathtakingly artful switching of vital props and set and especially keyboards to provide different locations is brilliantly orchestrated on the Watermill's tiny stage. And the whole is equally brilliantly lit by lighting designer Robbie Butler, with a glowing mosaic of colour that blends to create that sultry exoticism as the action heats up.