Marilyn and Ella, Theatre Royal, Stratford, East LondonThe Living Unknown Soldier, Arcola Theatre, London

Black ambition, blonde power

True, it's not as counterintuitive a coupling as Marilyn Monroe and Albert Einstein (who are imagined trading insights about relativity in Terry Johnson's Insignificance), but Monroe and Ella Fitzgerald also seem an improbable pair.

The iconic sex goddess and the first lady of song are filed in separate compartments in the collective mental archive of popular history. Bonnie Greer was inspired to bring them together in her funny, stirring and warm-hearted play-with-music by a tiny item on a TV documentary about Monroe. It mentioned that Monroe had pulled strings and helped Fitzgerald to perform at the Mocambo, the biggest – and whites-only – club on the West Coast. She persuaded the management to break its own colour bar by promising to sit in the front row every night. "Marilyn Monroe was ahead of her time and she didn't even know it. I owe her a debt," said the singer.

Marilyn and Ella intriguingly points up the affinities and contrasts between these ladies – both misfits with abusive childhoods and forlorn ambitions (Fitzgerald longing to break into the movie world that Monroe, vainly courting the legitimate Broadway stage in the mid-Fifties, now despised).

They are beautifully played by Wendy Morgan, who goes way beyond caricature in her complex impersonation of Monroe, and Nicola Hughes, who brings a knockout voice and charismatic dignity and humour to the part of Fitzgerald.

Before the pair meet, the double-hander and Colin McFarlane's production feel bitty, the constant switches of focus on the split-level stage offering a witty but a little contrived crash course in Monroe's unsung credentials and the women's complementary predicaments. The drama and the musical numbers ignite once we reach the historic gig at the Mocambo, as Hughes tears the place apart with an inspired, scat-singing rendition of "Mack the Knife" and serenades Monroe with a tender private performance of "My Funny Valentine".

On the starlit roof of the club, they exchange moving home truths about the exploitation of black artists by white fans and the true basis of self-worth and beauty. After that, elation knows no bounds when the two, clad in campy matching gowns, let teasing rip as the gold-diggers from Gentlemen Prefer Blondes. The jazz trio, led by Warren Willis at the piano, play up a storm.

An arrestingly fresh angle on familiar territory is also granted in the new show at the Arcola, presented by the imaginative Simple8 company. It's usually taken for granted that an "unknown soldier" is a dead soldier. What, though, if a combatant were to return from the front physically alive but "unknown" in the sense of being mentally oblivious of his past life and his identity? Conceived by the director, Sebastian Armesto, and based on a book by the historian Jean-Yves Le Naour, The Living Unknown Soldier takes its cue from the true story of an amnesiac French soldier in a psychological limbo at the end of the Great War.

Languishing in an asylum, he is claimed by hundreds of French families as their missing relative for a variety of reasons ranging from the crudely financial to the painfully emotional. The eight-strong company endlessly role-swap as this piteous, largely silent figure sits centre stage and is bombarded by the jabber of competing allegations. It's a device that eloquently communicates how he becomes a blank screen on which the world projects its own priorities.

Tom Mison is dashingly droll as the journalist who turns the unknown soldier into a careerist campaign, and then, having shown no interest in the truth, comes close to identifying him. And Tony Guilfoyle is excellent as the doctor who looks after this patient through years that are chalked up like a prison sentence until, with bitter irony, the German army in the Second World War starve the soldier and his fellow inmates to death. Recommended.

'Marilyn and Ella', to 15 March (020-8534 0310); 'The Living Unknown Soldier', to 15 March (020-7503 1646)