Maxine Peake is no blousy Blanche DuBois. One could almost call her steely, if only she didn't shatter like glass by the end of Sarah Frankcom's firmly feminist, modern-dress production of A Streetcar Named Desire. It's an astonishing performance, ripe with contradictions. Peake makes her a puzzle.

Outwardly, she's still recognisably the breathy Southern belle, clad in floaty floral dresses, who is forced, by misfortune, to stay in her sister's small studio flat in downtown New Orleans and so suffer her brutish new husband Stanley Kowalski (Ben Batt). But, though she's as wistfully romantic as ever, there's another side to this Blanche as well: stern and scolding – the schoolmistress she once was. Imagine a mix of Margaret Thatcher and Marilyn Monroe – the Iron Lady and the ingénue – in a single person. In time, the two personalities pull her apart like wild horses.

Peake is a Blanche who gives as good as she gets, at least for a while. Her clashes with Batt's Stanley aren't at all sexual, but serious and sharp. Only, wracked by guilt and drink, haunted by a silent chorus of Mexican flower sellers – the play's symbol of death – she's not quite strong enough to stand up for herself or for Stella. Arriving at Elysian Fields in the old empire blue jacket, her hair a blonde bouffant, she's shocked at its squat-like state – mattresses on the floor, mini-fridge at the side. She's not disgusted for herself, but appalled for her sister; a right-wing romantic, incapable of believing anyone could live like this.

It builds to an extraordinary confrontation. Having chosen to slum it with Stanley, Sharon Duncan-Brewster's Stella insists that she doesn't need rescuing, but Peake's Blanche is adamant that she shouldn't put up with domestic abuse. Pallid and gaunt, Batt might lack Stanley's animal magnetism, but he can be wolfish when he wants to be. It's an argument with no right answers: Blanche's moralising looks meddlesome, but she's right to see Stella's victimhood.

Played on the vast green baize carpet of Fly Davis's design, a symbol less of life's gambles (though Blanche's chips are down) and more that the whole flat is Stanley's domain, Frankcom's production is richly complex. It never neatens a choppy play, but teases out its contradictions. We get flashes of Monroe in Peake's coy flirtations with Youssef Kerkour's Mitch – a straightforward, but never stupid, big gent. She so wants to be romanced, but she's still horrified by men; a mark, perhaps, of her time at the Flamingo. Even if Frankcom finally lays it on a bit thick, dressing Peake as a Disney princess for the climactic rape scene, it makes for a chilling disintegration: not a woman overpowered from the outside, but torn apart from within.

A Streetcar Named Desire runs at the Manchester Royal Exchange until 15 October