The late duke, a £1.5m Freud painting, and a friendship that lasted 50 years

Glimpsed, half finished, in the artist's studio, the wife of the late Duke of Devonshire fell in love with a distinctive Lucian Freud painting. And yesterday the work, which is thought to have cost her husband up to £1.5m, was unveiled in a special ceremony at Chatsworth House in Derbyshire.

Glimpsed, half finished, in the artist's studio, the wife of the late Duke of Devonshire fell in love with a distinctive Lucian Freud painting. And yesterday the work, which is thought to have cost her husband up to £1.5m, was unveiled in a special ceremony at Chatsworth House in Derbyshire.

He had seen the painting, a distinctive portrait of the rear view of a horse, only in a catalogue of Freud's last exhibition at the Wallace Collection in London.

But in what must have been one of the more expensive decisions of his life, he gave the go-ahead for its purchase - only to die in May before the canvas was delivered.

Now it marks the final testimony of the friendship between the Duke and Freud, which endured more than 50 years.

The pair shared passion for horses and the races. It was a run of good luck with one particular horse, Park Top, that enabled the Duke to buy several of the paintings that now grace Chatsworth, one of Britain's most famous country houses.

"Skewbald mare" is the 14th Freud to enter the Devonshire family collections, in addition to a mural Freud painted on a bathroom wall during one visit. "My father was a collector by nature and by instinct," his son, the 12th Duke of Devonshire, said as the painting was formally unveiled by the art critic Robert Hughes in the ground-floor corridor where it will be on public display. "He improved the collection with his early spotting of the genius that is Lucian Freud."

The two men met in the 1940s long before Freud acquired the tag of Britain's greatest living painter. They were introduced by Lady Anne Tree, the Duke's sister, and shared a set of friends, revolving around Ann Fleming, the wife of the writer Ian Fleming.

"Lucian Freud is very good company, very stimulating company," the current Duke said. "He is very lovely and has a number of good friends who he has been friends with for a long time."

As a consequence, the Devonshires became part of Freud's coterie of sitters. At the 11th Duke's request, Freud painted his sisters, Elizabeth Cavendish and Anne Tree, before producing portraits of the Duke himself and his wife, now the Dowager Duchess of Devonshire.

The current Duke was painted in around 1962. "I sat for him one summer when I was at university, but when I went back to university he gave it to them unfinished rather than trying to get me back again," he said.

David Dawson, Freud's studio assistant whose photographs of Freud at work are currently on display at the National Portrait Gallery, said the portraits had stemmed from the friendship.

"He wouldn't ever have done a commission. He would have done it from an artistic point of view that he really wanted to paint a particular person."

The Duke said that it was sad his father was not there to join the celebrations. But it was a "thrilling" moment.

"This Freud was bought with passion. My mother was utterly besotted with it from the first time she saw it, months ago, unfinished, in Freud's studio in London," he said.

"She was insistent and despite our pleas to desist, she won the day. My father was completely with her. 'Go for it' were perhaps the most expensive three words of his life."

Although the Duke refused to say how much they paid for the work, reports suggested it could have been as much as £1.5m. He did not rule out buying any more Freuds, but admitted that the family would have to be similarly "besotted" to do so because they were increasingly prohibitively expensive.

Freud is expected to visit Chatsworth to see the painting in situ at a later date.