"You all know me" says Effie, the young woman in Gary Owen's searing, blind-siding monologue about the welfare state. And maybe you have come across a version of her: usually drunk by 11am, she staggers, swearing and threatening, through her home streets, causing her body, mind and neighbours havoc.

It's impossible to avoid Effie's stare: blunt and provocative, it burns out at the audience as she revisits her epic nights out and her monumental hangovers and demonstrates her reckless, fractious, violent energy. She's all Jagerbombs and pitchers of vodka martinis topped up with a bottle from the corner shop.

Then a chance encounter in a bar with a war-torn soldier changes her direction. She thinks it's not a one-night stand, he's got other ideas. And she is left – but not alone; now there's Effie and a baby growing inside her, and she begins to re-asses everything.

But for someone like Effie, in somewhere like Splott, a second chance is never an easy thing to get hold of and the play's chilling climax demonstrates the way in which we let those most vulnerable down.

Owen's play is inspired by the Greek myth where king Agamemnon sacrifices his daughter for the good of the state. Here Owen has swapped Greece for Wales but it could be anywhere. It's a raw, real, gut-punching wake up call, a play that demands that we look, and act, before it's too late. Owen's fluid text mixes street slang into an intense poetry. The imagery feels both familiar and oddly alien, like when, in the dead of night, Effie comes across two ‘gypsy horses' on the roadside. Iphigenia in Splott will linger with you, like a strange dream, for days.

In Rachel O'Riordan's brilliantly taut production for Sherman Cymru Sophie Melville plays Effie in a performance that crackles. She provokes both disgust and empathy and reminds us of the way we, and society, are so quick to jump to conclusions about people we know nothing about. A superb turn in a devastating play that will shake even the most sure-footed of us.

Iphigenia in Splott runs at the Temporary Theatre at the National until February 20.