Kate Valk leads the way up a winding marble staircase, past video screens showing unspeakable acts of body modification, to an empty room at the top of London’s Institute of Contemporary Arts. She pulls up two red plastic chairs and sits herself down on one, her laptop open on her knees. The videos are part of an edgy multimedia tribute to Kathy Acker that sprawls across the ICA’s lower floors. Valk is here to add a final theatrical flourish, directing a previously unstaged script by the pirate queen of 70s and 80s counterculture.

With its ornate cornicing and makeshift furniture, this deserted chamber could be a set for the Wooster group, the New York-based theatre ensemble to which Valk has belonged for the last four decades. Screens are everywhere in their shows, and at one moment – when trying to demonstrate the way in which she works – Valk puts her laptop down on the bare floor and starts to speak directly to it. “I can facilitate an encounter with the text,” she says. “This. Is. An. Encounter.”

Though unknown to the wider world apart from through a couple of film cameos, most recently in Jonathan Demme’s The Manchurian Candidate, among Wooster Groupies, Valk is a legend. Described by one admirer as “the Meryl Streep of Downtown”, she has been a constipated, comically unco-ordinated Phedre (To You, The Birdie!), a blacked-up Brutus Jones (The Emperor Jones), a Betty Boop-ish Dr Faustus (House/Lights).

Her most recent London appearance was in The Town Hall Affair at the Barbican last year, wreaking merry havoc as the radical lesbian Jill Johnston, one of the participants in a celebrated 1971 face-off between Norman Mailer and Germaine Greer. But all her attention today is on how to make sense of the late, great disruptor Acker.

The great disruptor … Kathy Acker. Photograph: Standard/Rex/Shutterstock

Though this isn’t a Wooster Group show, she has flown in with two young colleagues – another will join them later – for a collaboration with three UK-based performers, who were auditioned over Skype. The six have just three weeks to animate Desire, a mashup of dialogue, prose and stage directions, in English and French, featuring a roll call of potty-mouthed Shakespearean characters, and a walk-on for Wuthering Heights’ Heathcliff.

“I didn’t pick it; it picked me,” she says. “I don’t know what I’m trying to do yet, but this is a unique opportunity for me to have my moment as a director.” Then she corrects herself in the curious vocabulary of the Wooster Group, saying she is not the director but the instigator. “I like the term ‘instigating a performance’,” she says, “but, as a 62-year-old person with a lot of experience, I’m in charge of the instigation.”

It is the latest phase in a “late-stage development” that began in 2014 when Valk, who had never previously directed, turned the tables on Wooster Group founder Liz LeCompte, who doesn’t usually perform, by directing her in a piece inspired by a 1976 album of Shaker songs. Early Shaker Spirituals was followed three years later by another record-inspired piece, The B-Side: “Negro Folklore From Texas State Prisons”.

Desire is different, not only because it is being put together is such a short time and will run for only five performances. “It’s also exciting to me because this is not a theatre, it’s an arts organisation. So I feel at liberty to explore myself in a different way,” says Valk.

Both the Wooster Group and Acker were idiosyncratic stars of the late-20th-century New York avant garde, but that doesn’t mean they inhabited the same space. Valk joined the Wooster group aged 21 in 1979, talking her way into lodgings above their theatre, The Performing Garage in SoHo, on the promise of being able to make costumes and props. A few miles away, Acker was holding court with a different sort of performance, based on her own highly sexualised persona.

“There was something about her writing that was too aggressive for me,” says Valk. “I didn’t have the same relationship to sex. I wasn’t interested in taking on the male mind, getting inside it and taking it down. I’d gravitated towards a group with a woman in charge. The theatre was where I lived both in body and metaphorically.”

But, on a visit to London in the late 80s, she was intrigued enough to take up an invitation to meet Acker at the Groucho club and was surprised by how “incredibly warm” she was. Maybe, she muses, “something in her writing wasn’t available to me at the time. It’s interesting to come back and confront that and to see what my way in is, because this is not just going to be an encounter with the text. I have to have a very intense encounter with Kathy Acker. That’s what the Wooster Group is all about: when we take on a project we have to investigate the whole ethos of the writer.”

Does she feel afraid? “That’s the big question,” she laughs, snapping shut her laptop. “I almost said no to this, and there’s a huge risk of failure. But I only feel fear when I’m not working. As soon as I get in the space I don’t worry, because you just have to deal with what’s really happening.” And besides, she says as we head back down past the flickering screens, “this is a fabulous situation. It’s like the exhibition has done half of the dramaturgy for us.”

• Desire: an encounter with a play by Kathy Acker is at the ICA theatre, London, 31 July-4 August, as part of I, I, I, I, I, I, I Kathy Acker.