The middle-aged dentist in Clifford Odets’ Rocket to the Moon is brought up sharp by a visiting entrepreneur: “Years of dentistry have gone to your head.” The man’s touching 40, and his life is going nowhere. Or wasn’t, until the new secretary turned up.

Ben Stark (Joseph Millson) has been married for ten years to Belle (Keeley Hawes). They lost a baby and have been squabbling ever since. Her father, Mr Prince (Nicholas Woodeson), wealthy and widowed, with a penchant for Heifetz playing the violin, calls by to add insults to injury, and tops that by trying to date the delectable Cleo Singer (Jessica Raine), who has fallen for the boss.

It’s New York in 1938, it’s summer, and it’s very hot, though you wouldn’t know any of those things from Angus Jackson’s torpid production. The American accents are so dreadful you wonder why they didn’t just set the whole thing in Wycombe and be done with it. The dental surgery designed by Anthony Ward has a meaningless corridor taking up space and a battery of lights that are never used.

But the play itself is so captivating, and so well written, the callowness of the acting – whoever thought Keeley Hawes could be a tough Jewish wife with so little stage experience; why does Woodeson keep going into bad Groucho impressions? – is just about bearable.

And Jessica Raine, once she gets over a desperate bid to be funny and gawky in a role that could have been written for Marilyn Monroe, is really quite touching as a little lost girl who wants to be loved and craves a whole full world, with all the trimmings.

The play slides craftily from Ben’s menopausal crisis into Cleo’s bid for affection and meaningful occupation, fighting off Mr Prince, the wolfish Willy Wax (Tim Steed) and settling into a mature agreement with Ben, who closes the play with a shake of his head: “What I don’t know would fill a book.”

Millson is the one actor fully at home in the idiom of the play, and he strikes a full range of emotions while revealing a full set of splendid gnashers, as befits his calling. And Peter Sullivan as another dentist, sharing the surgery, at least hints at the Depression era with his empty appointments book and addiction to Scotch coffee.

The play, which seems forward-looking in themes and comic language (Arthur Miller, Neil Simon and countless American film comedies are all anticipated) is so rarely seen – last at Hampstead Theatre in 1982, directed by Robin Lefèvre – you’d want to catch it, even though you might ask, “Odets, where is thy sting?”