Why do women kill their children? Usually, these days, to protect them from the world. In Euripides's Medea, the displaced princess – she's a noble savage and descended from the sun god – commits infanticide to ruin her husband's life; she's already ruined her own.

This was more or less the sense of it when Diana Rigg played an Almeida Medea in a metallic, battering revival over twenty years ago. Today's Almeida Medea (Kate Fleetwood) is somebody quite different, a contemporary writer tortured in her solitude, boiling with a different kind of rage entirely, whose marriage to an actor, Jason, is dust.

Their Brazilian house-cleaner surveys an all too familiar scene of Islington domestic meltdown and a parade of lady neighbours bearing toy dolls and schmoozing along to Britney Spears suggest the air of cultural dislocation and emotional angst felt by someone who simply doesn't fit it.

This is all powerfully conveyed in Rupert Goold's production, the clipped, rapid dialogue of adaptor Rachel Cusk (a novelist who has made much of her own marital misfortunes in a memoir) and, especially, the ferocious, utterly self-absorbed and uncompromising performance of Fleetwood. It's pay-back time. She's spent fifteen years living with a complete stranger, she says: "You've taken away my history."

With Justin Salinger's flip Jason– "I've fallen in love with someone else, that's all" – she embarks on the opposite of marital harmony in some of the most savage, unpleasant domestic mud-slinging I've heard in some time, and this is the core of Cusk's text. Like Marina Carr with Hecuba at the RSC, she's written a terrific new play that tells you much more about herself, and the way we live now, than about Euripides, or indeed the characters who are more victims of political and mythical history than they are of their own.

This is the nub of it. A similar fallacy was at work at the heart of the Almeida's Oresteia – for me, The Bakkhai has been the absolute pick of the Greek season – that you release the heart of these great plays by dragging them into our own lives, instead of going towards them and colonising them more unexpectedly and more interestingly. It's not just a question of setting. It's a question of tone, poetry, the structure of the narrative, the flavour and perspective. I reckon the National came closer last year with Helen McCrory on a sliding scale between Greek grandeur and domestic anomie.

As Fleetwood stands, masking her extraordinary beautiful face with a curtain of her own hair, the opening exchanges between the nurse and the tutor are distilled as a clucking, funny meditation on maternity – delivered with blank indifference by Amanda Boxer and Andy de la Tour (who doubles later as Creon) – which Medea scythes through with contempt and ill feeling.

Her grey kitchen is fitted with a work space in the shape of a tomb. Later, Ian MacNeil's designs acquire a more blood red dimension, with the sound of waves crashing on the shore of Islington-on-Sea. It's hard, in either context, to see the point of Richard Cant's entertaining Aegeus, the king of Athens who offers Medea an escape route but who, in Cusk, is a prattling professional sell-out contemplating adoption with his male partner.

Medea's two young unnamed sons — on opening night, Lukas Rolfe and Sam Smith -- are well written and confidently played. Too bad they are pawns in the parental chess game they echo at their own childish level; and hard luck, perhaps, on being done out of a Euripidean ascent to the sun on a golden chariot with their vindictive mum.

Medea runs at the Almeida Theatre until 14 November