It begins as a distant roar, echoing through the dingy, grafitti-wrecked landings and stairwells. Beyond doors sealed with nailed planks and padlocks lie desolate floors and shadowy vaults, where industrial green chutes stand silent behind chainlink fencing. Across just such a floor, in what was, until the 1990s, the biggest postal sorting office in London, lies Kuba, the Turkish artist and film-maker Kutlug Ataman's installation for Artangel.
Kuba is also the name of a shantytown slum, wedged between tower blocks and the airport in Istanbul. Ataman spent more than two years getting to know the wary, suspicious inhabitants of this illegal, mostly Kurdish neighbourhood, and filming them talk. Forty of these monologues are shown on 40 television sets, each old, portable, junked technological behemoth sitting on its own stand. In front of each TV is a sagging, second-hand armchair. The voices of the people of Kuba - young and old, women and men, defeated and defiant - are with us now. They smoke, they cry, they sing; the subtitles churn through their tales.
Each screen is a talking head, someone sitting at a kitchen table or in a cramped sitting-room, equipped for the most part with just the kind of old furniture we're sitting on. Ataman, invisible behind the camera, occasionally asks a muffled question, but these people don't need much prompting. They've got a lot to talk about.
The longer you listen, and the more you meander from chair to chair, the more you gather that these stories are entwined, in betrothals and blood feuds, jail-time and dead time, which the unemployed men spend in makeshift coffee houses, the women stuck with their kids, or waiting outside the prisons for their husbands' return. Sometimes, they don't come back.
There are drinkers and devout Muslims, thieves and one-time revolutionaries, gamblers and crazy people. The kids have their turf wars, they steal, they do drugs, they have their pitiful fantasies. Here's Ugur with his backwards-facing baseball cap, his winning smile and his dreams of inventing a new type of car. Yalcin who went away to a religious school and got into drug-dealing. Yuksel the cuckolded wife, Raziye and Safiye who long for an education, a way out. Nejla the football-playing tomboy who's probably a lesbian but doesn't know it; Eda crying with her kids, old Emine who lost her children to heroin.
The women often turn to Hatun for support, defiant Mother Hatun, with her gold teeth and her smoker's face and her wonderful eyes and her filthy tongue. Mother Hatun talks about being beaten: "The doctor asked what happened to my face and hands. 'What's it to you?' I said, 'What you should ask is what happens to the women in prison whose newborn babies are cut and thrown in the toilet.' " Sometimes, sitting close to the screen, the floor opens up.
Kuba is a tight-knit place, and these people are in many ways better off - say - than the street kids of Rio and the dispossessed of many other of the world's expanding cities. Kuba isn't - quite - the City of God. According to Ataman, it is a state of mind - rebellious, lawless, cohesive. One inhabitant says that when he first arrived he found a community that was like a village, a family, where no one took account of language, religion or race. Some say it is charming, and speak of the shanty with obvious affection. No one knows why it is so called - it is named perhaps after Cuba, a distant, chimeric ideal. For all its awfulness, its inhabitants feel a deep sense of belonging: "I live here too," one woman says, "So I can't say it's bad even if it is."
Here's Dogan, who read and read and turned himself into a Marxist - after hanging around for a while with fascists (at least he thought they were fascists - "they had 'interesting moustaches' "). Dogan is dogged by his former police torturer, whom he keeps running into in the restaurant and at the horse track.
The stories told by Kuba's 40 characters are often terrifying. In Kuba you can be arrested for writing a petition, for playing Kurdish music at a wedding, or even for buying a magazine. The men go away to "special prisons", or get tortured in the local police station. Police torture is considered almost normal. It comes up again and again, a shadow cast on many of these soliloquies. Then there are the petty feuds, the wife beatings, the crime, the poverty and ignorance.
Places like this surely exist in many cities. Kuba started as a goatherd's shack in a stony pasture. It was followed by another shack, then another. Mud walls and masonry and corrugated iron. We don't see the outside, except for a roof of vine leaves in Hatun's yard, and the glare of daylight beyond a curtained window. Some here say that they have never seen the sea, which is just a short distance away.
Kuba is Ataman's finest work to date. His videos and films have always concerned themselves with the stories people have to tell - aging opera divas, Turkish transsexuals, an Englishwoman obsessed with lilies, people who believe in reincarnation and women who wear wigs. Kuba is many lives, more than a cast of characters, in that after a while one begins to form a bigger picture of their interconnections, shared difficulties, common struggles and complex betrayals. Kuba begins to have the richness of a novel: a mosaic of truths and lies, insight and ignorance, anger and humour and humanity.
There is a lot of specious talk in contemporary art about "breaking boundaries". Mostly, this is inconsequential blather. In this work, Ataman has overcome what I have often previously seen as the limitations of his staging. Moving outside the gallery, and opting for the most basic technological format (never mind the DVD player concealed in the cabinet beneath each television), Kuba succeeds in a way his more apparently sophisticated installations do not. Here, one faces his characters as though we were seated opposite them, as though we were their guests. We are also constantly aware of the bigger picture, stretching away all around us. It is a babble of intimacies.
The jumps and the edits are visible, and the translation makes these people appear highly articulate, which I have no doubt many of them are; equally, many are illiterate and have had barely any formal schooling. Often, their Turkish is poor.
How political a work is Kuba? Ataman told the Guardian recently that Kuba is his rejoinder to a show like The Turks at the Royal Academy. Kuba is, he says, a history. It is perhaps trite to say that the political begins with the personal, but it does, as these testimonies reveal. The stories these people share remind us that politics cannot be escaped. For the people of Kuba, that is not an option.
· Kuba is at the Sorting Office, 21-23 New Oxford Street, London WC1, until May 7. Details: 020-7713 1402. www.kuba.org.uk