Hanna, Arcola Theatre, London, review: Beautifully performed by Sophie Khan Levy

This one-woman show, engrossingly written by Sam Potter and beautifully performed by Sophie Khan Levy, pulls us into the experiences of a young mother who discovers that her three-year-old daughter is not hers genetically. An alcoholic nurse had accidentally swapped her birth daughter, Ellie, with another newborn girl. Hanna got pregnant by her “strong but silent” school pal, Pete, just before she was due to take up a place at university. But she has never resented the shift of plan because she believes that motherhood has altered her life for the better – more profoundly than a degree ever could. So when Pete starts to accuse her of having been unfaithful – Ellie's complexion looks too dark to him – it's a terrible blow that the DNA test reveals that Ellie isn't hers either. It forces Hanna to confront the question of what motherhood means. Is the “real” mother always the birth mother? Is it a bond made up of genes and blood or one created by care and devotion?

The script and Khan Levy's portrayal have a lovely unforced naturalness. Hannah is shy and conciliatory but charmingly honest and straight even while nervously signalling her awareness that trust can sometimes be misplaced and taken advantage of. George Turvey's well-paced production is simply staged – just a chair, rug, jug of water and glass – in a way that seems to merge counselling session and chat show. Not that she is out to claim any special status for herself. Hanna's discourse is constantly seeking to bridge our experience and hers: “Have you ever had that moment?...”.

Nature or nurture? What is the force of class and ethnicity and income level on parenting? Hanna is inclined to blame herself when things go wrong and it only exacerbates this tendency when she meets the other family who are wealthy and mixed-race and she has to contrast her “little three-bed in Hemel” with their seven-bed mansion (“It was like being shown round the Cluedo board”). She's young, working class, has little support and wouldn't know how to go about finding a lawyer, let alone sue the hospital for compensation as this other family are planning to do. Ought money to give a couple more clout in cases of mix-up like this?

Potter writes with particular finesse and empathy about the conflicted feelings that are aroused in Hanna when the two little girls (who have been told nothing) start to have sleepovers at each other's houses. She muses on her intense bond with Ellie, the one she raised, and her deep, regretful connection to Ayesha, the one she lost. Ayesha has a wobbly patch at Ellie's place at the first of these and Hanna can't prevent herself crying along with her. The child is weeping for her mum; Hanna is sobbing because she thinks that it is all her fault and that she has let this child down badly from the outset. Bouncing on the bed lifts both their spirits, until Ayesha slips and has a bit of an accident.

In general, the relationship seems to be going well, but there are intimations of unease. My problem was not with the mounting panic, which is well sustained, but that the 70-minute play feels rushed and too positive in the way that it winds down from this peak. Nonetheless, well worth seeing.

Until 20 January (arcolatheatre.com)