Tom Varey as Ollie Olsen and James Tucker as The Yachtsman
Tom Varey as Ollie Olsen and James Tucker as The Yachtsman
© Alex Brenner

Within a few days we've had stage versions of unproduced screenplays by America's two greatest playwrights. Arthur Miller's The Hook at Northampton is followed by Tennessee Williams's One Arm at Southwark, an episodic mini-epic of a mutilated, beautiful boxer who becomes a male prostitute. Now on death row, and prompted by a lifetime of letters, he revisits his own past.

Whereas Miller's story fell foul of studio bosses (and the FBI) on account of its politics, Williams's 1942 short story, written around the same time as his first stage success, The Glass Menagerie, was only "performable" in the permissive 1960s, which is when Williams wrote a screenplay draft.

Nothing happened till ten years ago when Moisés Kaufman fused story and screenplay for Steppenwolf in Chicago. Kaufman's play resurfaced off-Broadway in 2011, and now Josh Seymour directs the British premiere.

The piece retains a shocking frankness about sex for money, and one-armed Ollie Olsen – a welterweight champion in the Pacific Fleet cruelly injured in a car crash – combines familiar Williams traits of the damaged gigolo and the Apollonian athlete, the living piece of antique sculpture.

As he turns tricks on street corners and adopts a gay bar hustler lifestyle in New Orleans and New York that accelerates into pornographic movies and a murder count, he's too much, in the flesh, of an outline rather than a real character, though RADA graduate Tom Varey gives him a strong and centred propulsion through the sketchy 75-minute narrative.

Williams never wrote a dud line which is why anything of his is always worth seeing, however imperfect. Kaufman starts with direct quotes from the screenplay, indicating scene-settings and "dissolves" and the play never shakes off this handicap any more than does The Hook at Northampton get away from its cinematic straitjacket.

But as always in Williams, the honesty of the writing never dwindles into special pleading. Ollie is frank and practical in the services he provides, and his clients are frank and practical in their needs. Even the girl in the movie – Georgia Kerr also gets to play a nurse and a stripper – evinces a generosity of spirit in her variously humiliating service industries.

Joe Jameson is even more versatile, playing various studs, a drag queen madam and a divinity student who calls by the cell for one last salvage attempt and finds the tables turned on him. And James Tucker plays both a sad sack, unreliably toupée-d middle-aged client in a Central Park apartment and the sleazy filmmaker on his yacht, totemic figures in a piece best viewed as a pre-Aids prequel to Angels in America.

One Arm runs at Southwark Playhouse until 4 July