Marlene Dietrich has a famous name – but, as a star from the golden age of 1930's Hollywood, she is beginning to fade from living memory. So Peter Groom’s portrayal of her in Dietrich: Natural Duty is a welcome reminder of a woman who was not just a screen goddess, but led a fascinating life across Germany and America in the Nazi era.

This show focuses not merely on her stage and screen appearances, but primarily on her role entertaining US troops through the Second World War. Taking the form of “An Audience with…” show, Dietrich runs through her career, singing some songs and telling some stories. But she is interrupted from time to time by offstage questions from a determined journalist, who forces her to delve a little deeper than she had planned.

Groom plays the part in drag, a decision which could have gone in one of two ways. You might be expecting something over-the-top and kitsch, but Groom avoids that by playing a straight bat – and his height and presence accentuate the larger-than-life persona of the glamorous Dietrich. In truth, as with any good performance, you cease to notice who is playing the role, and just see Marlene Dietrich in a quite fabulous dress. (Under the lights it looks stunning.)

In the earlier scenes featuring the young Dietrich, Groom seems constrained – as if he is holding himself back a little. But he is wonderful as Dietrich the performer; you can sense him relax into the part as she entertains the troops, involving the audience, relishing the innuendo in a knockabout version of “See What the Boys in the Back Room Will Have”.

The depth of the play lies in Dietrich's complicated relationship with Germany. Nazi propagandist Joseph Goebbels is unhappy about her determination to go and work in America, reinforcing his encouragement to stay and make films celebrating the new Germany with ominous knowledge of Dietrich’s mother’s address in Berlin. Dietrich’s response is unambiguous: she returns to America and takes citizenship.

Her wartime service entertaining Allied troops contrasts with the drama of trying to locate her mother in Germany. But this second strand is allowed to lapse and, though it gives an emotional punch to the conclusion, I felt there was a missed opportunity for an ominous undercurrent that would have maintained more tension through the play.

The ending doesn’t come when you expect it to, and we see another unflinching side of Dietrich – but Groom plays her with a subtle sense of doubt, in a nuanced and thoughtful characterisation. The audience lapped up the songs and the jokes throughout; this is an absolute crowd-pleaser of a show.