Franz Xaver Kroetz is Germany's most produced living playwright – a fact that may or may not explain why his work is so little seen in this country. On the basis of The Nest, it ought to be staged a lot more.

Written in 1975 and subtly updated in a new translation by the playwright Conor McPherson, this quietly devastating study focuses on a couple embarking on parenthood. Martha and Kurt might be the young marrieds Theresa May was thinking of when she talked about making life better for ordinary people.

They are just that. Ordinary. Like you and me. Struggling to make the best of their lives, and to get by. In one long scene, Martha goes through her baby list, item by item, from the buggy with a window in the rain hood to the aloe vera oil that will prevent stretch marks. The bill mounts up but Kurt is not deterred. "Approved," he shouts with excited joviality, kissing the baby bump in tender affection.

That determination to do right by their child whatever the cost infects the couple's life with poison - both literal and metaphoric. Alyson Cumming's effective set hints at the unease; there's damp rising from the floorboards of the tiny, tidy flat. The foliage surrounding it both represents another better world, and the onset of the jungle. PJ Harvey's magnificently atmospheric score and Gregory Clarke's detailed sound design set it adrift in the sounds of a city.

At one point, Kurt pauses to listen to a passing siren. "I always love it when you hear a siren pass by. You always think ‘It's not me'." But as the couple struggle to survive, those dangerous sounds come closer. Kurt takes on more and more overtime for extra cash; Martha is left alone to bring up a new born child. Even a beautiful day out is marred by the thought of the money lost to leisure. "Do you want for anything?" Kurt asks, hurt. "Just my husband," Martha replies.

You have the terrible sense – as in I, Daniel Blake – of how close many people are to the edge, a pay packet away from doom, ground down by the endless need to find money to make ends meet. Ultimately, the relentless grind of trying to keep the family's head above water drives Kurt to a reckless act – which has terrible repercussions for them all.

I felt that act tipped the play into melodrama, but I still admired the way it doesn't seek easy solutions. It twists and turns bleakly on the moral dilemmas both Kurt and Martha face. And although the text asks us to make the jump and see society's values themselves as tainted by consumerism and uncaring capitalism, Ian Rickson's finely-tuned production grounds this insistent message in heart-felt naturalism, turning a slow, deliberate gaze on what desperation looks like.

The performances from Laurence Kinlan and Caoilfhionn Dunne have the same touching reality. You believe in these people, their happiness, their suffering and their dilemmas and their final moments on stage, reaching for the future, are as tentative and unresolved as life itself.

The Nest runs at the Young Vic until 26 November.