Hockney’s 1972 work Portrait of an Artist (Pool with Two Figures) was described by Christie’s in New York as “the holy grail of his paintings, from both the historical and the market perspectives” before it went under the hammer.

The previous record for a work by a living artist was set by American Jeff Koons for one of his Balloon Dog sculptures which sold for $58.4m (£45.6m) in 2013.

Portrait of an Artist was sold to an unknown buyer and the identity of the seller is also unconfirmed.

Bradford-born Hockney, 81, was inspired to paint the picture by two photographs he found on his studio floor, one of a swimmer in Hollywood in 1966 and another of a boy staring at an item on the ground.

His painting depicts two men, one swimming under water while the other watches from the side of the pool.

The standing figure is said to represent Hockney’s former partner Peter Schlesinger, whom the artist met in 1966 while teaching art in California.

For the next five years, according to Christie’s, Mr Schlesinger was both “the great love of Hockney’s life” and one of his favourite models.

Hockney had already begun the painting when they split up in 1971. After a break, he resumed the piece the following year.

Alex Rotter, co-chairman of post-war and contemporary art at Christie’s in New York, said the painting reflects both the European and the US perspectives of Hockney who went to live in California in the 1960s and saw himself as living on both continents.

He said: “It has all the elements that you would want in a Hockney painting.

“The California landscape, the beautiful trees and flowers and the sky, and then what we know him most for, which is the pool.”

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