In a large, deserted post-office sorting room in central London stand 40 aged televisions, testament to the time when such things were known as “brown goods”. They stretch out across the space, each screen filled with a different close-up, the room buzzing with 40 voices as each face tells us the story of their life (there are English subtitles). The stories can take hours to unfold; to hear them all would mean days in this bunker. This is the latest project from Artangel, the group behind Rachel Whiteread’s House and Jeremy Deller’s Battle of Orgreave. It is called Küba.

The reference is not to Castro’s island. The Küba in question is a dirt-poor enclave outside central Istanbul. A squatter camp set up by left-wing Kurdish radicals in the 1960s, it later drew outsiders of all kinds, from crooks to religious fundamentalists. It operates under its own contrary rules; violence is common, but nobody needs to lock their front door, as the neighbours never steal. Few in Istanbul’s burgeoning city centre know it exists. For the artist Kutlug Ataman, it represents “an island of identity”. “We should be aware that there is somewhere like this in every city we live in,” he says.

Shortlisted for last year’s Turner prize, for his video installation Twelve — in which Shi’ite Arabs who believe that they have been reincarnated tell their story — Ataman is a Turkish-born naturalised American who now lives in London. He left Istanbul in 1980 after being imprisoned for filming outlawed leftwingers. Küba is his biggest homeland project since.

“When I was visiting Istanbul, a friend of mine who eventually became my producer lived nearby,” he explains. “What was interesting for me was that all my previous pieces were dealing with subjects who were fabricating certain identities in front of the camera. I was always interested in the machinery, how they were doing it. This time, it was more like a community, working together, creating this one identity, which was quite surreal: this neighbourhood that calls itself Küba.”

Similar spaces exist across Europe, spaces where the outside world’s rules hold no sway: Kristiana, in Copenhagen; the squats in St Pauli, Hamburg; the parts of Rimini operated by Spiral Tribe; isolated pockets of King’s Cross, in London. But they are all in retreat. Even Amsterdam is re-considering its lax drug rules and late-night opening, preferring to toe a more conservative line. Istanbul is no different.

“I wanted to capture Küba before it went, to preserve the contemporary history of the place. Because we all know that one way or another, sooner or later, the place is going to disappear.”

Ataman nods. “To me, it’s like trying to close down Venice Beach, in LA. Who are we to close anything down? And Küba is not the only shanty town in Istanbul. Until recently, most of the people who came to the city from the country had to start shanty towns. They had no other choice. It is our greatest hope that it won’t be dealt with in an aggressive manner, as in the past, when they sent in the bulldozers.”

Ataman’s camera-work and interviewing are consciously naive. This can make for tiring viewing, but it suggests a raw honesty that allows the marginalised to speak with as unedited a voice as possible. “I want to tell these individual stories, which we would otherwise have no access to, not on TV or even in film documentaries,” he explains. “This is now the job of the artist, taking on the position, previously held by the media, of hearing people’s stories from their own mouths. After London, we will take the project to Stuttgart, Vienna, Sydney, bringing it to other cities where our perception of ‘the other’ is so singular and threatening. We are hoping to put the entire installation on a barge and have it travel along the Danube from Bulgaria to Vienna, the heart of old Europe, in the hope that it infects the pristine European narrative there. Hopefully, through this barbarian story, there is a new Europe that’s going to be created.” He coughs self- consciously. “I’m only pointing things out, you understand? I’m not claiming that a work of art can change the world.”

Küba, The Sorting Office, 21-31 New Oxford Street, WC1, from Tuesday until May 7; www.kuba.org.uk