Looking for the artist Anish Kapoor's new house in Chelsea, London, I decide he might be having a Turner moment. I was expecting a beautifully crafted modern house, with walls of glass, stone and shimmering stainless steel, designed by the architect Tony Fretton. What I didn't know was that all of this would be secreted behind a bland slab of speculative neo-Georgian design.  The painter JMW Turner set up home in Chelsea more than 150 years ago, when it was a poor and unfashionable suburb - but one where wonderful light was cast every day over the Thames. The Indian-born Kapoor belongs to a very different generation of British artist, one that thrives on celebrity. In moving to Chelsea, he has chosen to make his family home in what is now one of the most expensive and least bohemian parts of London.  Kapoor and his wife Susanna's Notting Hill home was designed by an architect friend, Pip Horne, in the late 1980s, so the idea of building a new house was not in itself a challenge. What was new was the idea of a modern house hidden from the street - "as you might find in Paris or Barcelona," Kapoor explains. A passage below the neo-Geo flats leads you into a world of unexpected courtyards, gardens and trees. There are enormous rooms, sudden stairs, cleverly constructed views and a richness of low-key materials. The narrow entrance gives way to a star-shaped courtyard, open to the sky. The kitchen and dining room are at one end of this courtyard; the other is faced, down a few wide steps, by a long living room. This is as much a private art gallery as a space in which to relax or entertain.  "The idea of the courtyards was a given, really," says Kapoor. "This is a long, narrow site and we wanted to get as much daylight into the rooms as possible. The idea developed so that the house became a way of walking in and out of fresh air and gardens, on the way from one side to the other."  Kapoor has collaborated with a number of architects over the years; a series of striking curved and mirror-finished entrances for subway stations in Naples, which he developed with Future Systems, will open later this year. His most radical work on an architectural, and indeed monumental, scale has been in partnership with the structural engineer Cecil Balmond. Their Marsyas sculpture, installed in Tate Modern's Turbine Hall in 2002, was an extraordinary stretch of voluptuous red fabric. Next year, another Balmond-Kapoor project will transform the Middlesbrough landscape: Tenemos, a kind of voluminous windsock stretched between apparently delicate posts, is the first of a series of five vast public artworks, with sites in Stockton, Redcar, Hartlepool and Darlington next in line. "All these projects," Kapoor says, "are about interrogating form, and making large-scale objects that manage to be as ethereal as they are substantial."  Where Kapoor's sculptures are often richly coloured and sensuously formed, his new home works around a limited palette. At first glance, it is as cool as a cucumber. "I am naturally playful," Kapoor agrees, "while Tony [Fretton], though he has a dry sense of humour, can be almost comically dour." The principal rooms have been designed for books and artworks. These, and family life (the Kapoors have two children), will provide all the colour needed. Fretton has worked with Hopton Wood limestone and Mandale Fossil stone, two materials much loved by British sculptors and architects since the 1930s. Hopton Wood limestone, quarried near Matlock, Derbyshire, is creamy, warm and studded with fossils; Mandale Fossil limestone, from a quarry close by, comes in shades of grey and is immensely hard-wearing.  Kapoor and Fretton have known each other for years, since the artist's work was first shown in the Fretton-designed Lisson Gallery, in London. "We've enjoyed a healthily detached relationship," says Kapoor. "As a client, you need some sense of distance from your architect. I thought of keeping out of the way while he built the house - he's a craftsman by nature and very involved in construction - but I couldn't help myself, and ended up coming down nearly every morning on my way to my studio in Camberwell."  Kapoor doesn't intend to work from home. "The house is a quiet object," he says. "This is a family home, not a place for me to make a mess - I have a studio for that. For me, architecture is about the essentials of light, space, proportion and materials. I don't want to live in a sculpture designed by an architect. I go crazy when I hear people say that the best new sculpture is by architects - meaning overexpressive buildings. I love making sculptures, and collaborating with architects, but I want to live in a house that's a happy home, not an artwork."  Kapoor says that if he could have chosen any architect in recent history to build him a house, he would have chosen Louis Kahn. "No disrespect to Tony. Kahn is long dead, and anyway, I'm not sure I would be able to live up to one of his designs. He made everyday buildings somehow mythic, and my family and I need a healthy dose of reality to make everyday life comfortable. Tony and I also share a huge admiration for the work of [American conceptual artist] Dan Graham, and this house is partly a homage to him. We'll be installing a Graham pavilion in the garden courtyard here, so house and artwork will play off one another."  Fretton has designed homes and studios for artists throughout his career. From the Lisson Gallery in Marylebone, through the Camden Arts Centre (in 2004), via modest and beautiful spaces including the Holton Lee Studios on the Dorset coast, Fretton's subtle designs have been handmaidens to modern British art. Each is quietly powerful; none gets in the way. Kapoor describes his own home as "a reflection of a quiet modern vernacular". "It has traditional rooms, even if some are pretty big. And, look, we've even got skirting boards! They're made of strips of stainless steel rather than traditional timber, but which modern architect would put skirting boards in a new house? They hate them."  In a sense, Fretton and Kapoor are following in a tradition of creating just such houses in Chelsea - artists' homes that play a subtle game of balancing new and age-old designs, plans and building materials. In the late 19th century, artists such as William Holman Hunt, Dante Gabriel Rossetti and John Singer Sargent came to live and work in Chelsea. A generation of radical artists and architects (Richard Norman Shaw, CR Ashbee) teamed up to shape the look of the area. The 1921 census reveals that nine out of every 1,000 people living in Chelsea was an artist. Today, the borough has become so expensive that the Chelsea College of Art and Design has left, moving to Westminster.  Will the artists return here? If they make Hirst-loads of money, perhaps. In the meantime, Kapoor's secret hideaway, a brushstroke or two away from Turner's old house, is a fitting retreat for a contemporary artist quietly in love with the best - but not the noisiest - modern architecture.
A passageway through a nondescript block of flats leads Jonathan Glancey to the artist Anish Kapoor's new home: a quiet oasis filled with sculpture, light and green spaces