Whenever she leaves Cuba, the authorities tell her not to come back. What does the Cuban artist have in store for Tate Modern’s Turbine Hall? Will the mounted police have to be called out again?

Tania Bruguera, the Cuban artist and activist, is sort of talking about a project she shouldn’t talk about. She is the latest artist to take on Tate Modern’s Turbine Hall commission – its details a secret until the installation is opened with theatrical flourish on 2 October. And she is enjoying the suspense: she has been dropping tantalising clues on her Instagram account that take the form of images of well-known paintings. Clue No 1 is Caillebotte’s Les Raboteurs de Parquet, an impressionist work from the 1870s that depicts three artisans scraping down the wooden floor in a bourgeois apartment. Clue No 2 is Holbein’s Ambassadors, which shows two beautifully dressed men standing next to a table loaded down with intriguing objects.

This is not really helping. My best guess is that the Caillebotte suggests something about shared, communal labour. I’m not sure what The Ambassadors hints at, since it’s such an enigmatic work of art.

“My God, I have never done this before,” Bruguera says, gleefully, “this thing of saying nothing and saying everything. Let’s say that this work is related to portraiture.” She gives me some other clues. It will, she says, be the first work in the Turbine Hall commission’s 18-year history to be a community project. Or, more specifically, a neighbourhood project, since it will involve people who have Tate Modern’s postcode, London SE1. She likes the idea of its not being about communities but neighbours, those people you can’t choose, often don’t meet and who might range through every socioeconomic bracket.

She drops a few more hints. It will involve a legacy, a shift in the way the Tate works, a new body that will outlast the project itself, called Tate Neighbours. As with all Bruguera’s creative output, it will rely on others for it to burst into existence. “It will need the audience to uncover the work, to reveal the work. It will only exist if there is a genuine collective effort to make the work happen. To make it you have to work with people you have never met. Unless you come together with 300 friends, you will have to work with whoever is next to you. It is a neighbourhood in the Tate.” And what is it all for? “It is about how we make immigrants our neighbours. That is the big question of the project.” It is, she says, her response to the rising global tide of nationalism and xenophobia.

Facebook Twitter Pinterest Tania Bruguera at Tate Modern. Photograph: Linda Nylind/The Guardian

The audience will reveal the work. It will only exist if there is a genuine collective effort … To make it you have to work with people you have never met

For Bruguera, who is 50, art, activism and politics are not matters to be carefully untangled and set apart. Her work is always in the service of a political idea. It is arte útil – useful art. She grew up in Cuba in a well-connected family. Her father served as a diplomat, loyal to the regime to the end of Fidel Castro’s life. She studied in Cuba and the US, and her life is largely divided between the two countries.

She considers herself a revolutionary, but has become a thorn in the side of the Cuban authorities. She has been detained repeatedly, interrogated on more than 40 occasions, and denounced in newspapers as a CIA operative.

She is currently campaigning against law 349, which is due to come into force in December and has been condemned by Amnesty International. It states that artists must have a permit from the culture ministry to undertake any artistic activity. “That means you cannot just exhibit paintings in your home, or do an alternative theatre play. These are called artistic services and you have to ask permission. The government is saying it has to be art that fulfils revolutionary ethics. Of course, they never explain what revolutionary ethics are.” Inspectors are sent round to check up, and infractions can lead to fines or confiscation of artists’ IDs – the official licences they already need to operate. Does she still have her ID? “I still have it. They wanted to take it but I had an exhibition at MoMA [in New York] and it was hard for them to justify it,” she says.

Facebook Twitter Pinterest What if … Tatlin’s Whisper #6, performed in Havana in 2009. Photograph: Solomon R Guggenheim Museum, New York Guggenheim UBS MAP Purchase Fund, 2014

The work she considers her most successful is a piece called Tatlin’s Whisper No 6. (The series of works is named after Vladimir Tatlin, the Soviet constructivist artist.) At the Havana Biennial in 2009, in the wake of Raúl Castro’s promise of a greater degree of open debate in Cuba, she set up an official-looking stage, presided over by two men in military uniform. Anyone could step up to the podium and say what they wanted for one minute. A white dove was placed on each speaker’s shoulder – a reference to the dove that landed on Fidel Castro’s shoulder in Havana in 1959 when he spoke amid the triumph of the new-minted revolution.

Tatlin’s Whisper No 6 was, she says, “the art of ‘not yet’, or the art of ‘what if’”. Taking official statements on openness at face value, she created “a real moment of free speech. And it worked because it stopped the government. They didn’t know how to censor it. I don’t like to be censored. I want to make work that surpasses censorship.” The piece, she says, is her most theatrical work. “I staged reality. And this is the only thing they understand – theatre. Not performance but traditional theatre, where the script is prewritten and there are just a few stock characters.”

A recurring motif of her recent interrogations has been the Cuban authorities urging her never to come back

She once had an argument about the theatre of Cuban politics with her interrogator. (She has one regular woman assigned to her.) These sessions might involve being taken to a police station or a special house; frequently they happen when she is entering or leaving the country. (A leitmotif of recent interrogations has been their urging her never to come back.)

“It is frightening,” she says. “You feel in those moments that the law doesn’t exist. It’s an interesting position to be in because it was the first time I have felt the law – I mean the absence of it. You assume in your life that certain protections or rights exist. When I asked for a lawyer, they said to me, ‘You have been watching too many Hollywood movies.’ I said, ‘I want to call my family.’ It never happened.” She is normally filmed during these sessions, which she finds unnerving: she fears the footage will be manipulated.

Facebook Twitter Pinterest Video: police horses in action, for Tatlin’s Whisper No 5

You have to treat the Turbine Hall not as a gallery, but as a street. Maybe people pass by and stop. Maybe they just pass by

Bruguera, for now, is concentrating on the Turbine Hall commission. She has already made one work in the space – not for the big annual project but as part of the museum’s regular programme. Unheralded and unpublicised, it involved two real mounted police officers using crowd control techniques on visitors. She liked it because it was simply itself, rather than a representation or a symbol. They were real police officers, doing to visitors what they did to crowds in reality. If her work sounds dry and conceptual, this is the artwork to knock aside that view: it was alsobeautiful, the horses splendid and incongruous in the museum. “I have had to forget that piece in order to do this project. I just kept thinking, ‘It has to be better than the horses!’” she says.

Her favourite works in the Turbine Hall series have been “the ones that everyone loved” – Doris Salcedo and Olafur Eliasson. Salcedo had a crack jackhammered into the length of the Turbine Hall; Eliasson’s Weather Project involved artificial fog and a strange, hovering sodium sun. Looking back at her predecessors in the series, she has learned that “you have to do a clear gesture instead of objects. And, no matter what you do, people will make it their own in their imaginations. You have to treat the Turbine Hall not as a gallery, but as a street. Maybe people pass by and stop. Maybe they will just pass by.”

Facebook Twitter Pinterest Immigrant Movement International, a 2012 performance work in Tate Modern’s Tanks.

The world is catching up with Bruguera’s view. Many younger artists are rejecting the fastidious distinction between art and activism; they are nailing their colours to the mast. Art, Bruguera argues, has a role to play in responding to a political situation, or to precipitating change. Sometimes a response to injustice is not primarily rational, but emotional; emotion that can then be processed into language or music or art, she argues.

Bruguera’s work can be dark, but there is also a chink of light. “Sometimes I deal with negative energies. That does not mean the work is pessimistic, but that it deals with things people would rather not touch. I do work with faith. I have faith. It’s just that the path is complicated.”

• Tania Bruguera’s Hyundai Commission is at Tate Modern, London, from 2 October-24 February.