A Francis Bacon portrait of Lucian Freud not seen in public since it was first exhibited 57 years ago is to be auctioned with an estimated price of more than £35m.

Sotheby’s on Wednesday announced what is believed to be the most valuable contemporary work to be offered in London in almost a decade.

Study for Portrait of Lucian Freud was painted in 1964 and shows Freud with his chest bare and face monstrous and mangled, sitting on a hard bench with his arms outstretched and his fists clenched.

It is based on a black and white photograph taken by the two artists’ mutual friend John Deakin and shines light on a friendship and rivalry that was incredibly intense, but ultimately incredibly bitter.

The painting was the central panel in a triptych exhibited in 1965 in a travelling exhibition to Hamburg, Stockholm and Dublin. With Bacon’s consent, the triptych was broken up, with the left-hand panel now in a private collection and the right-hand one in the Israel Museum in Jerusalem.

Bacon and Freud met in 1944, introduced by the painter Graham Sutherland. They became instant friends and in the 50s and 60s they would see each other almost every day, both in each other’s studios as well as eating and drinking in Soho’s most celebrated haunts.

The Guinness heiress Caroline Blackwood once said she remembered having dinner with Bacon every night for the five-year duration of her marriage to Freud in the 50s.

Freud was the sitter in 1951 for Bacon’s first identifiable portrait of an individual. He went on to paint Freud more than any other person, save himself.

By the 80s they were drifting apart because of petty rows and jealousies, with Freud clearly tiring of Bacon.

Freud’s daughter, Bella, said of the feud: “I was rather disappointed that they weren’t friends when I then started spending more time with my father and sitting for him in the late 70s. When I asked him why he fell out with Francis, he said ‘because his work went off’. But I am sure there was more to it than that, because they had been so close and obviously seemed to love each other.

“Francis was clearly somebody who he adored and admired. And there weren’t many people my father talked about in that way. The things he repeated about him were just dazzling, utterly disarming and breathtakingly wonderful, and silencing because of their brilliance. I imagine he must have missed that when he stopped being friendly with him.”

Bacon’s remark on the fizzling of the friendship, told by a smiling Freud to William Feaver, his biographer, was: “She’s left me after all this time. And she’s had all these children just to prove she’s not homosexual.”

The work has been in the same private collection for 40 years and will go on public display at Sotheby’s galleries in New Bond Street London from 23-29 June.

It will be auctioned on 29 June in a sale titled British Art: The Jubilee Season. Other works include Banksy’s portrait of Winston Churchill with a lime green Mohican, estimated at £4m-£6m; and David Hockney’s almost 4-metre wide portrayal of Woldgate Woods.