The Container, Young Vic, London

The earnestness of being imported

Is there a more uncomfortable theatrical experience to be had at the moment than watching The Container? Suddenly the cramped seats, claustrophobic foyers and endless queues of the West End's creakier theatres seem positively luxurious.

In keeping with the current trend for all things site-specific and immersive – not least in the Young Vic's last production, the thrilling Kursk, which plunged audiences into a murky world of sonar beeps and submariners in a radically-transformed Maria studio – The Container takes place within the tinny, stuffy confines of a container lorry.

Clare Bayley's play about immigrants smuggling themselves into the UK was the word-of-mouth hit of the Edinburgh Fringe in 2007. Now the co-production with Amnesty International has pitched up in London in the form of a rusty, dull-blue metal box parked outside the Young Vic. Before the play starts, audience members are divested of heavy coats and bulky bags and handed a small bottle of water before being shepherded, in a compliant crocodile, on to The Cut. Lined up outside the "venue", we are instructed to sit on the wooden pallets, tuck in our feet and – if it all gets a bit much – "just bang on the door and someone will let you out". The airless lorry seats only 28, lined up like anxious, lightly roasted sardines against unyielding, bumpy walls. The door bangs shut behind the last. A bolt slides across.

The first few minutes are truly horrifying. In pitch darkness, the silence is broken only by the insistent, nausea-making vibrating sounds of a lorry in motion. After what feels like an eternity, the noise stops and a flashlight shines out of the black. Torches are the only lighting used in Tom Wright's production, often shining directly into the eyes of the audience as the action unfolds in a narrow, dusty strip down the middle of the container. It's all hugely uncomfortable – which is the point, of course.

Bayley's play puts us firmly and unforgivingly in the same position as her characters – human cargo on the run from private and political traumas in their homelands of Afghanistan, Somalia and Turkey. All harbour hopes – some vain (a job serving the Queen in Buckingham Palace), others humble (to see a wife and child once more) – of a better life and a new start in an idealised Great Britain.

All five have their own plans, their own secrets and their own strategies for maintaining their dignity in the most crushingly, squalidly undignified of circumstances as they scrap over scraps of food, jealously guard their few valuables and lie to one another. We hear them vomiting and defecating in the darkness though, fortunately, the only smell we experience is the acrid stench of their desperation. When the shadowy "Agent" (a bulging-eyed Chris Spyrides) who has stowed them in the lorry, arrives with supplies, his weaselly demands for more money reveal the lengths each will go to in order to reach their goal.

The performances are necessarily intense. In particular, Doreene Blackstock as Fatima, the Somali matriarch of the truck, sparks nicely off Abhin Galeya's laconic, mysterious Jemal. Bayley's script feels a little underwritten, though, too abruptly concluded and too quick to leap on vague narrative hooks of scrapes with the Taliban and unspecified refugee camps at the expense of any real depth of characterisation.

As a striking crystallisation of the migrant experience, The Container is memorable and vital. But it's the suffocating, blindly-ignorant darkness of those first few minutes, over and above any words or performances, which stays with you long after you step out, blinking and thoroughly relieved, on to the street.

To 30 July (020 7922 2922; www.youngvic.org )