The 12ft by 6ft Beverley Hills Housewife, by David Hockney, is part of the collection amassed by Betty Freeman, the American philanthropist and patron of the arts, who died in January.

A David Hockney painting called Beverley Hills Housewife which could fetch a record £7 million at auction went on public display yesterday.

The 12ft by 6ft work is part of the collection amassed by Betty Freeman, the American philanthropist and patron of the arts, who died in January.

Housewife depicts a 1960s California woman - Ms Freeman - standing on the patio of her luxury home.

Hockney produced the work between 1966 and 1967, shortly after arriving in Los Angeles, where he visited Ms Freeman to paint her swimming pool for some pieces that became the California Dreaming series.

It is expected to be sold for £5 million to £7 million, which would beat the current record for a Hockney, the £2.92 million paid for The Splash in June 2006.

Laura Paulson, Christie's deputy chairman and international director of post-war and contemporary art, said: "Beverly Hills Housewife is one of the artist's most fascinating and iconic works and remains a perfect, timeless tribute to Freeman, a modern-day Medici, who will be remembered as an influential patron of our contemporary culture."

Housewife is on show at Christie's in King Street, central London, until Thursday - only the second time the work has ever been displayed in the UK.

The painting will be sold in New York on May 13.

In addition to the Hockney, Christie's New York Post-War and Contemporary Art Evening Sale will feature works from Ms Freeman's collection by Roy Lichtenstein and Andy Warhol.

A total of 19 lots from the collection are to be sold, with a total estimate of £18 million to £28 million.