In Belgrade, audiences cut her; in New York, they came in their thousands and wept. What will happen when Marina Abramović lands in London for her most radical show yet? Emma Brockes talks to the art superstar about lipstick, masochism – and why she's too much for any man

In 1974, Marina Abramović did a terrifying experiment. At a gallery in her native Belgrade, Serbia, she laid out 72 items on a trestle table and invited the public to use them on her in any way they saw fit. Some of the items were benign; a feather boa, some olive oil, roses. Others were not. "I had a pistol with bullets in it, my dear. I was ready to die." At the end of six hours, she walked away, dripping with blood and tears, but alive. "How lucky I am," she says in her still heavy accent, and laughs.

This June, Abramović, who at 67 sometimes refers to herself as "the grandmother of performance art", will open an exhibition at the Serpentine Gallery in London, her first original performative show in the UK, in which, she says, she will be more daring and more vulnerable than she was both in Belgrade and at MoMA in New York, four years ago. Then, Abramović sat in a chair in the gallery for eight hours a day, while visitors streamed in and, one by one, occupied the chair opposite her. Some wept; others laughed. At least one took off all her clothes and had to be removed by security. For three months, Abramovic sat there, impassive, during which time The Artist is Present drew record crowds to the gallery and became one of the most famous and controversial pieces of performance art ever staged. Fox News got very cross about what it all meant and referred to her as "some Yugoslavian-born provocateur," while a curator at the Whitney Gallery called her "one of the most significant artists of the second half of the 20th century." For her part, Abramović sat. And sat. And sat.

Now here she is on a dull morning in a studio in Brooklyn, dressed head to toe in Givenchy, her favourite designer, and nibbling on what looks like a pellet of astronaut food. For her Serpentine show, Abramović has to be fit, both mentally and physically. She is on a strict diet, and will shortly be leaving for Brazil to meet up with some sort of shamanic adviser. She'll need it; the London show, which is called 512 Hours for the duration of time she will spend in the gallery, will remove even the few shreds of structure the MoMA show clung to. No chair this time, and no table. Instead, all day every day from 11 June to 25 August, Abramović will wander around the gallery where, after being asked to shed their coats, watches and all their devices, visitors will be invited to come in and peer at her. "It's the public and me and nothing else," she says. "I took the objects away. But the encounter ..." She smiles. "I've never done anything as radical as this. This is as immaterial as you can go."

'There's nothing more tragic than artists from the 70s still doing art from the 70s.' Photograph: Mike McGregor

When performance art is bad, it is worse than almost anything and even the good stuff is vulnerable to ridicule. It looks like nothing on paper; a woman wanders around a gallery – where's the artistry in that? Those tempted to scoff should watch the HBO documentary on Abramović's MoMA show, to see how an unpromising premise turned, in reality, into an extraordinarily moving series of encounters. Since her early days in Serbia, Abramović has put herself under extreme physical and mental duress to jolt viewers out of ordinary patterns of thinking. "The medium is the body," she says, which is what all performance artists say, but when Abramović cuts herself with a knife, or slams her body into a wall, it is done with such purity of purpose the viewer is lifted temporarily out of themselves. It is the opposite of sensationalism or exhibitionism – a gesture of self-erasure in the Romantic sense – and to sit still for three months, inviting connection with strangers is something that, in the context of the harried and distracted lives we live, makes perfect sense. No wonder people cried.

"You have to be in a state in which you are completely secure about your ability create this kind of charismatic space," she says, and is currently lying awake at night "in total panic" about doing it again at the Serpentine. "That's really hell."

It is only recently that any of this has hit the mainstream, and Abramović as rock star – as well as knocking around with Lady Gaga, who she helped develop strategies to stop smoking (such as counting grains of rice), she is on the cover of fashion magazines and her Maria Callas-esque profile on the way to becoming iconic – is the fruit of a 40-year struggle. For decades, Abramović was poor and beyond the art world, obscure, living out of a van for the best part of 10 years with her then life-partner, Uwe Laysiepen, a German artist who performed under the name Ulay and with whom she drove around Europe, collaborating on her seminal work of the 70s. (The van, incidentally, was tracked down and displayed at the MoMA retrospective, which caused Abramović to completely freak out. "That van," she says, and shudders).

When she and Ulay broke up, it was in grand style: they turned the death of their relationship into a piece called The Lovers (1988), in which they walked towards each other from two sides of the Great Wall of China – 2,500km each, over the course of several months – meeting in the middle "to say goodbye". If that's not devotion to one's art, I don't know what is.

Abramović came out of a tough background. Her parents had close ties to the post-war communist regime of what was then Yugoslavia and her mother raised Abramović in a home run more like a boot camp than a family. In 2011, she turned what amounted to an abusive upbringing into a stage production called the Life and Death of Marina Abramović, co-starring Willem Dafoe and Antony Hegarty of Antony and the Johnsons, and in which she played both herself and her mother. "Every rehearsal I cried from the beginning to the end," she says. "Then one day Bobby [the director] said, enough of this bullshit crying. The public has to cry, not you. After three years of touring in Europe, I was free. All these stories don't affect me any more. An incredible feeling."

This was after years of critiquing the repressive nature of both her family and her country through performance art. In her piece The Lips of Thomas (1975), she carved a five-pointed communist star into her own abdomen, a monstrously sly up yours to the regime and appropriation of brutality for her own purposes. In other gallery settings, she and Ulay slammed into each other, shrieked in each other's faces, or sat staring at each other for interminable lengths of time to test, and conquer, the boundaries of what is endurable. It was thrilling, shocking, above all, moral and sailing always in the face of accusations of meaninglessness. The great danger with this sort of art, of course, is that pain is mistaken for meaning.

"In the beginning there were just masochists doing this shit and it was ridiculous. They needed to go to a psychiatric clinic," she nods. "It's more complicated to explain. In every culture, [there are those] shamans or medicine men who endured incredible physical pain, because it's a door opening to the subconsciousness. And the way we can actually control the pain – it's how to control everything. This is the key."

The experience at MoMA would have turned most people mad – sitting still for that length of time, neither speaking nor moving. (There was a concealed hole in her chair, with a chamber pot fitted beneath it, so she didn't have to get up to go to the loo). Abramović was not daydreaming. The whole point of the exercise, she says, was to be fully present, concentrating on connecting with whoever came in to sit down opposite her, and "I never saw so much pain in my life." The huge number of people who wept, she thinks, was brought on by this staged situation in which "there is nowhere to go except in yourself. It was shocking. But how simple it was."

Before the show opened, both Abramović and MoMA half worried that no one would turn up. As the thing took off, celebrities started to drift in to sit opposite her, including, inevitably, James Franco – and then Ulay came. Abramović broke protocol and reached out to grasp his hands across the table. Everyone cheered. "I absolutely didn't expect he'd come to sit. The moment he sat – and everyone got very sentimental about it, because they were projecting their own relationships on to us – but it was so incredibly difficult. It was the only time I broke the rules."

What is her compulsion to move towards, rather than away from the things that most terrify her?

'Working with the British public is particularly hard. They're very sarcastic. They're easily bored.' Photograph: Mike McGregor

"From a very early time, I understood that I only learn from things I don't like. If you do things you like, you just do the same shit. You always fall in love with the wrong guy. Because there's no change. It's so easy to do things you like. But then, the thing is, when you're afraid of something, face it, go for it. You become a better human being."

What's the cost?

"Ah, a big one. Lots of loneliness, my dear. If you're a woman, it's almost impossible to establish a relationship. You're too much for everybody. It's too much. The woman always has to play this role of being fragile and dependent. And if you're not, they're fascinated by you, but only for a little while. And then they want to change you and crush you. And then they leave. So, lots of lonely hotel rooms, my dear."

Ulay and Abramović split up in part because she was moving ahead of him as an artist, something he reflects on rather bitterly in the documentary, saying caustically that she became "very ambitious" after they separated. Abramović has been slammed by some of her peers for making money and dressing in couture, when her whole career has been dedicated to anti-materialism – her least favourite era was the 90s Brit-art scene, with its "commodification of art".

She has no time for this. "I've been criticised by my generation, artists from the 70s – and there's nothing more tragic than artists from the 70s still doing art from the 70s – because I blur all these borders between fashion and pop. I really got angry yesterday, because there was a lady who said 'Marina is not serious because she wants a fashion magazine cover.' And because I did an event with Jay Z. She said I'd killed performance art. But who made these rules?"

Anyway, she says, "I love fashion. Who says if you have red lipstick and nail polish you're not a good artist."

Her art is still deeply anti-materialistic. It is hard to package and sell performance art, which is why she was drawn to it in the first place. The nearest you can get is video or photographic stills of her now iconic shows. In 1974, when she invited the public to use those objects on her frozen figure, Abramović exposed a savagery lurking beneath the surface of otherwise civilised human beings. At first, visitors to the gallery were hesitant to approach her. Then, in a kind of Lord of the Flies scenario, they started subtly to torture her. "There still are scars from where the people were cutting me," she says. "They were taking the thorn from the rose and sticking it in my stomach. The public can kill you. This is what I wanted to see."

But at MoMA, the transactions were loving.

"Yes. I understand that you can bring out the worst in people and the best. And I found out how I can turn that into love. My whole idea at MoMA was to give out unconditional love to every stranger, which I did. And the other one [in Belgrade] was a challenge to every bad energy possible; if you give the guy a chain saw ... you are provoking him."

'I dream to have this perfect man, who does not want to change me.' Photograph: Mike McGregor

Incredibly, just before she started the sit-in at MoMA, she began divorce proceedings from her then-husband, Paolo Canevari, the Italian artist. "At the end of the project he came back, for a year. Even more terrible. Nothing worked any more. It was – god – endless. But there is a part of you in these periods that is numb. You are totally blank."

Is she in a relationship at the moment?

"No. Of course, I dream to have this perfect man, who does not want to change me. And I'm so not marriage material, it's terrible. But my dream is to have those Sunday mornings, where you're eating breakfast and reading newspapers with somebody. I'm so old fashioned in real life, and I'm so not old fashioned in art. But I believe in true love, so perhaps it will happen. Right now, no, I have no space. But life has been good to me. Lots of pain. But it's OK."

It is an intensely weird way to live and she knows it. How things will work out at the Serpentine, she doesn't know. British people are so inhibited, she says, and also inclined to ridicule. She is perhaps remembering what happened to David Blaine when he suspended himself in a Perspex box above the Thames all those years ago and was rewarded with jeers and people chucking bottles. But Abramović does not belong in his corny showbiz category. There is no illusion in what she does; when she cuts herself, it's real. The whole point is it's real.

Anyway, she says, "working with the British public is particularly hard. They're very sarcastic. They're easily bored. They don't want to be involved in anything that might embarrass them, or make fun of them. And that's a huge challenge." She is nervous as hell.

She is also looking beyond August to September, when she will stage another performance piece at Sean Kelly Gallery, her professional home in New York and beyond that to her 70th birthday party, which the Guggenheim has offered to host. "I'm really a warrior of art," she says, the kind of phrase only a woman with Abramović's background can get away with. "When I do things I do them properly, and then the other Marina comes and is very fragile and very vain and wants to eat ice-cream."

Or to put it another way, she says, "I love bad jokes. I love to enjoy everything. Then comes this moment to work – and it becomes a question of life or death."

• Marina Abramović: 512 Hours is at The Serpentine Gallery, London W2, from 11 June to 25 August.

• This article was amended on 15 May 2014. An earlier version said that the Serpentine exhibition is Abramović's first ever, rather than first original, performative show in the UK. She has, in fact, appeared twice previously at the Manchester International Festival.