Petra Karagy, a Macedonian woman, is furiously searching for her long-lost son, Alexander, who disappeared to England three years earlier; Shivan Rajagopal is a Sri Lankan doctor; Aziz is in flight from civil war in Algeria; Ameena is a Somalian refugee who was brutally raped and tortured.
Marshalling their conflicting claims to the right to asylum is immigration officer Simon Le Britten (a name that is one of the play's many painstakingly obvious notes of symbolism), who has himself found a kind of asylum in this job after being made redundant from the Post Office, where he was a middle manager.
One's credulity is frequently stretched by this gathering and the clumsy conflicts that the playwright provides for them. Wertenbaker's characters are types and viewpoints, not living, breathing creations.
But Sacha Wares provides a frequently arresting production, on a stunning maze-like design by Es Devlin, and it is acted with a fierce kind of commitment by a large cast (there are 11 in total) that includes the wonderful American actress Olympia Dukakis as Petra. She's the wonderfully sympathetic centre - passionate yet controlled - of this sometimes too dispassionate, rambling drama.