Yael Farber has just flown in from Mumbai and, even with jetlag, she's a talker. She's here because her adaptation of Miss Julie, August Strindberg's 1888 tale of class, love and lust, is about to open in London. Farber has relocated the action from a Swedish count's estate in the 1870s to the hot, steamy kitchen of a working farm on the Eastern Cape of South Africa on Freedom Day 2012. The play, called Mies Julie, was a runaway success at Edinburgh last year, winning the best of the fringe award, and prompting the Guardian's Lyn Gardner to say Julie "has never raged quite so fiercely as she does in this searing and fearless new version". In November, the production travelled to Brooklyn for an equally rapturous reception, making several critics' picks of the year.

Farber laughs at the memory of Edinburgh. "We were in a small, modest hall. The production values were quite low, and we had maybe three rows of people in the audience for the first couple of performances. I kept taping off most of the auditorium so that we didn't disperse them." Then the national press noticed the show and things really took off. "It was one of those Edinburgh stories," she says. "We all gave everything to this piece and it was an exceptional way for it to be launched."

Her adaptation centres on Julie, the Afrikaans daughter of a farmer in the Karoo region who goes looking for trouble, and John, a Xhosa servant on the farm whose mother, Christine, works in the house; her fingers are so worn that when she tried to vote, she had no fingerprints to prove her identity. Through their various interweavings, the realities of modern South Africa – particularly inequality and unemployment – are laid bare as the play hurtles towards a bloody climax. In Farber's hands, noted Gardner, John and Julie emerge as children so damaged by the past that it is impossible for them to forge any relationship in the present. "Do you feel free?" asks Julie. "Sure," says John, to which she commands, "Kiss my foot."

What drew Farber to Miss Julie? "Strindberg was looking at how psychosexual dynamics can unlock deeper issues of class and gender. There's that pendulum swing, that power play in any sexual dynamic, that enables people to say precisely what is on their mind. South Africa is post-dream: we're into the reality now. There's stuff that's said around certain dinner tables; stuff said in certain shebeens or pubs. But I was also interested in what was not being said."

A key part of the story centres on land: who does it belong to and how did they get it? "Land is the cornerstone of apartheid – the Group Areas Act, the Natives Land Act. Those acts were about taking land and enforcing control over it. Although the acts have been done away with, the symptoms are still around. But I didn't want to make an obvious 'that was stolen' or 'certain people have a right to it' narrative. John says, 'My people are buried here beneath the floor.' And Julie replies, 'Well, mine are buried out beneath the willow tree, three generations back.' That is the reality for a lot of families living and working on those farms."

In the original, Christine is actually John's fiancee, not his mother. Why the switch? "It was absolutely clear to me that she had to be the mother, because then the stakes are so much higher – and theatre is all about taking every human being to the full extent of what they're able to endure. Many of us, almost across the board as white South Africans, would have had a black mother in our homes who was as present as your own mother, if not more so.

"I'm generalising, but you were on her back as a toddler, while she cleaned the house. The intimacy is astonishing, and then this very strange separation happens, where you get trapped in a system of designated superiority, and this woman stays at that position. She gets sucked into a system that considers her inferior. And you go on to a life as a so-called superior human being."

Farber recalls the moment when Julie and John contemplate running away together. "But Christine," implores Julie, "we could be a family." Farber says: "It always gives me a chill when Christine replies, 'A family?' and Julie realises [the full implications of what she's saying] and tells herself, 'Sweetie – we are not a family.'" In this, Farber wanted to produce "on-the-nose writing, like when people have had a couple too many drinks or just had sex. It gives John the opportunity to say, 'That is my mother, not yours. That is my land, not yours.' And she can say, 'No, that's my land.'"

Farber, 42, was born and raised in Johannesburg. She recalls spending her teenage years sitting in the city's Market Theatre and witnessing the birth of protest theatre. "I remember feeling like it was the only place that was telling the truth and I will never forget that. It was like a fever." She went on to study acting and directing. One day while working as an actor, her friend Lara Foot (director of the Baxter Theatre in Cape Town and now the producer of Mies Julie) said to her: "When are you going to stop being an OK actress and take up directing?"

She did. And her production of British playwright Mark Ravenhill's Shopping and Fucking won her the prestigious Vita award for best national director in 1999 when she was 28. Since then, she has made other award-winning work: Molora, her South Africa-set reworking of Aeschylus's Oresteia trilogy, ran at the Barbican to critical acclaim. She has now relocated to Montreal, where she teaches at the National Theatre School of Canada.

Mies Julie's flashes of violence make me wonder what Farber thinks of the oft-repeated notion of South Africa's "culture of violence", trotted out again during the Oscar Pistorius pre-trial hearing. "South Africa is a brutalised society," she says. "And it is brutal. It is struggling to come to terms with itself and there are gaping wounds. But trying to see South Africa through the reflection of Oscar Pistorius is dubious. There's a sobriety there right now about what is going to happen to us. It's what it comes back to in Mies Julie: how far are the new generation going to be able to reinvent their narratives? Can John and Julie – and South Africa – transcend those narratives? They keep almost getting there then falling into potholes. I really wanted the audience to absorb that there is possibility. And I think there is possibility in South Africa."

Apartheid began when the National Party took control in 1948. Next year will be the 20th anniversary of the multiracial democratic elections that confined it to history. What does Farber think of it now? "It was just an epic fuck-up," she says. "A ridiculous, insane experiment that a small group of people imposed on a society – and, in all truth, a slightly larger community kept it in power through apathy. Thank God a movement wrested sanity from the iron grip of that system. The consequences are a society that is going to have to shed it, like layers of skin over generations."

She pauses, perhaps finally feeling that jetlag a little, before saying: "It's not going to happen overnight. You can't microwave this process."