Refugees desperately seek shelter, neo-fascist thugs roam the streets, a whole continent is threatened with chaos. Such is the background to David Greig’s richly resonant play, which makes a brilliant opening choice for Michael Longhurst’s new reign at the Donmar. If I didn’t know the play, from 1994, was the work of a Scottish writer, I’d have guessed it came from the pen of the Swiss-German master, Friedrich Dürrenmatt.

The setting is a defunct railway station in a small European border town chiefly known for its soup and lightbulbs. Sava and Katia, a father and daughter fleeing from war in the former Yugoslavia, settle in the station – and their presence is both a temptation and a provocation. Sava joins the stationmaster in a futile sit-in, and Katia forms a sexual bond with a female porter filled with romantic dreams of Europe. But the refugees also release the anti-migrant hatred of the jobless local youths.

First-rate performances … Natalia Tena, as refugee Katia, and Kevork Malikyan as her father, Sava, in Europe. Photograph: Marc Brenner

What makes the play so powerful is Greig’s hunger for a peaceful, unified Europe and awareness of the chilling reality: Sava talks movingly of the search for dignity, while a cynical entrepreneur views the border simply as “a magic money-line”. Longhurst’s production and Chloe Lamford’s design perfectly match the play’s ability to mix the minute and the metaphorical. Every detail seems correct, down to the railway timetables fixed with drawing pins, yet the station eventually comes to stand for a continent.

The performances are also first-rate and show how, in a time of crisis, unlikely alliances are formed. Kevork Malikyan’s homeless Sava discovers a touching affinity with Ron Cook’s redundant stationmaster wistfully recalling the days when you had “600 lives in your hands on an autumn morning”. Similarly, Natalia Tena’s peripatetic Katia, seeking stability, is ardently pursued by Faye Marsay’s porter for whom travel is an endless opportunity. At a time when our theatre seems fixated with America, it is refreshing to discover a play that not only reveals a deeply European sensibility but that also addresses the vital question of whether the continent can ever live up to its visionary ideals.

• At the Donmar Warehouse, London, until 10 August