Mike Nelson is feeling his age. He’s halfway through installing his new work, in the soaring Duveen galleries of Tate Britain, and as we sit down to chat, I notice the support strapped to his arm. The artist gives me a quick run-through of all the dislocations, injuries and strains that decades of vigorous construction work, all in the name of art, have exacted on his arms and shoulders. “I’m starting to feel long in the tooth,” he mutters apologetically.

It all feels apt, given the work he’s installing. Redundancy, decrepitude and physical labour are central themes of The Asset Strippers. In preparation, over the last six months, he has amassed an array of industrial equipment from British manufacturers downsizing, closing or moving out of the country. Shelved, archived, stacked, clustered and sitting on reinforced flooring, this collection of machines large and small recasts the London gallery as a storage facility for the detritus of British industry.

Positioned to echo familiar works by Eduardo Paolozzi, Anthony Caro and other greats of British post-war sculpture, these knitting machines, filing cabinets, cement mixers, drill bits and tractor treads are all arranged in stacks on low plinths throughout the halls. Many of the monumental metal remnants from the textile industry are still delicately threaded with ribbons, sequins and spools of coloured thread. While celebrated for their sculptural qualities, these objects are full of latent power: they’re not ready to stop working yet.

Facebook Twitter Pinterest ‘A storage facility for the detritus of industry’ … an exhibit in the show. Photograph: Matt Greenwood/Photo © Tate (Matt Greenwood)

“There’s stuff from old haulage companies,” says the artist, who has twice been nominated for the Turner Prize, “and from plastic, metal, woodworking, knitwear and textile industries. Farming is in there as well. To some degree, it’s dictated by what was around when I was looking: the work is based on online auctions, where they’re asset-stripping companies.”

Nelson, who is much more a creature of the analogue world, favouring film, carpentry and hand-making, has taken to haunting such auction sites, watching for items on sale. “I actually hate the internet,” he says. “I hate computers. So it’s hell.” But he is a devotee of science fiction and cites as an influence Roadside Picnic, the 1971 Russian novel about the traces left on Earth by an alien visitation.

Thanks to this book, written by the brothers Arkady and Boris Strugatsky, Nelson developed a fascination with the study of civilisation through its abandoned objects. Another influence is Solaris, Stanislaw Lem’s 1961 classic, in which space travellers discover a planet with an ocean that conjures up visions before their eyes. “In many ways,” says Nelson, “that ocean has become like the internet. Materials have been thrown out and I’ve got to make sense of them.”

Facebook Twitter Pinterest Spin cycle … a cement mixer in The Asset Strippers. Photograph: Matt Greenwood/Photo © Tate (Matt Greenwood)

Nelson’s breakthrough work, Coral Reef, was first shown in 2000, at Matt’s Gallery in London. This was sculpture as physical storytelling, eerie and immersive. It plunged visitors into a disorientating netherworld: a series of 15 rooms – the reception of a minicab office, the lobby of a budget hostel – leading from one to another. Throughout, there was a mounting sense of menace, an unspecified threat, that seemed to foresee the paranoia of the post-9/11 world. The Guardian called it “one of the true masterpieces of modern British art”.

Nelson, who is from Loughborough but now lives in London, is exquisitely sensitive to time and place. Months, and sometimes even years, in the planning, his otherworldly creations seem to have been generated seamlessly from the territory they occupy, and the artist has just stumbled on them. In Turin last year, a modish gallery in a post-industrial space was transformed into a dirt-filled drive-in cinema, with the interiors of its parked cars offering troubling biographies of their absent drivers. It was also a portrait of a country resting on old glories – car design, cinema. Nelson is a bit like Kate Adie, the former BBC war correspondent: if he turns up in your neighbourhood, it’s probably time to get out.

Nelson, 51, was expecting his first child while working on Coral Reef. “Now here I am, years later, and she’s about to leave home. You think, ‘Oh my God, where did that go?’” The same could be said for his art. “I’ve demolished most of it,” he says, “which I loved doing when I was younger, because the idea of it existing only in the memory of those who visited it was exciting. But, as you get older, it sometimes looks like a lot of hard work has just disappeared.”

Facebook Twitter Pinterest Breakthrough show … Coral Reef at Tate Britain. Photograph: Rick Colls/Rex/Shutterstock

A modern masterpiece: Mike Nelson's The Coral Reef | Jonathan Jones Read more

The Asset Strippers is not a companion piece to Coral Reef, but the two works do still perform as way-markers of a kind, for Nelson’s own life as well as for the shifting political climate. The paranoia foreshadowed in Coral Reef has played out and now Britain’s departure from the EU, and the warnings from companies, make The Asset Strippers feel very telling. Nelson did not wish to make a work specifically about Brexit but, he says, “you can’t ignore the timing of it and where you’re showing”.

Nelson’s labyrinthine work is never just about objects: it’s about the stories they carry, the people whose lives they were once part of. But The Asset Strippers has a personal connection: “I bought a lot of stuff from an electrical engineering company in my home town, where my cousin used to work and a lot of my friends’ parents, too. It’s been there for about 100 years, but it’s just been moved to the Czech Republic. You can sense the presence of the people who have worked on its machinery.” Circumstance has transformed this debris into sculpture.

“Some of the more rewarding conversations I’ve had have been with the lorry drivers delivering stuff,” he says. “They have a very good understanding of the material and what it means to them. Often, their ideas about Brexit are contrary to mine, yet their understanding of the problems facing Britain are not that dissimilar. They just have a different conclusion. I was pleased about that, because I didn’t want to make something that was dogmatic, but rather one that discussed the underlying structure that gave rise to this situation.”

In the 20th century, sculptures started to look like machines – and machines started to look like sculptures

Barricading and supporting the industrial artefacts is wood stripped by the Ministry of Defence from Victorian barracks, along with doors sold off from old hospitals by the NHS. Nelson wanted salvaged timber to keep with his theme of detritus, but found it hard to get the thousands of feet of old “four-by-twos” he needed.

“It’s a standard old building material that roofs and walls are built out of, but I was having a problem finding it.” All the old four-by-twos, it turned out, were being bought up by a single dealer and sent to China to be made into designer furniture, which was then shipped back to be sold as luxury goods. “The wooden materials,” says Nelson, “are part of the whole madness of it all.”

The Duveen galleries recently exhibited British sculpture from the 1950s. It featured offalish lobes by Henry Moore and a dead hen by Elizabeth Frink – a clotted form, stiff and unnaturally poised. There was also the skeletal Fisheater by Lynn Chadwick, which seemed as much fighter jet as diving bird. These were sculptures created when the fate of man and machine seemed ever more tied, when the brutal force of mechanical warfare was no distant memory. All were products of industrial transformation in Britain and beyond.

Facebook Twitter Pinterest Bygone world … an exhibit sits on salvaged timber. Photograph: Matt Greenwood/Tate

In the 20th century, says Nelson, “the sculptures started to look like machines and the machines started to look like sculptures”. The Asset Strippers takes the next step, raising the question of what happens to sculpture as manufacturing comes to an end, when a country no longer makes things.

Constructed in 1937, the Duveen galleries have an air of imperial grandeur that was vainglorious even then, as the British empire was breaking up. Like the sold-off machinery in The Asset Strippers, these galleries stand as a monument to an era that was already passing, giving them a mausoleum quality. Nelson says he is “cannibalising the last vestiges of industry”, which makes his vast work feel like a measure of where the country is at. Welcome to Britain, the fire sale.

• Mike Nelson: The Asset Strippers is at Tate Britain, London, until 6 October.