A nude painting of a pregnant Irish teenager by Lucian Freud, one of the most famous British artists of the 20th century, is expected to sell for up to £10 million at auction next month.

Sotheby's has announced that Pregnant Girl by Lucian Freud – estimated at £7 million-£10 million – will go under the hammer in the Contemporary Art Evening Auction in London on February 10th. The painting, dating from 1960-61, is appearing at auction for the first time.

Lucian Freud, who died in 2011, was a German-born British artist and a grandson of the Viennese psychoanalyst Sigmund Freud. He was a well-known figure in late 20th-century London, was married twice and is reputed to have fathered at least 14 children by several women.

After divorcing his second wife, the Anglo-Irish aristocrat Lady Caroline Blackwood (daughter of Maureen Guinness, Marchioness of Dufferin and Ava) in 1959, he embarked on an affair with an Irish teenager, Bernardine Coverley. She was 16 when they met; he was 38.

Coverley was the daughter of Irish parents who ran the Black Horse pub in Brixton. She was sent to a convent boarding school at the age of four. Later, the family moved back to Ireland but the teenage Bernardine ran away to London and met Freud in a pub in Soho. The couple had two daughters – Bella Freud, a fashion designer, born in 1961, and Esther Freud, a novelist, born in 1963. Pregnant Girl depicts Bernardine Coverley pregnant with Bella.

Oliver Barker, a Sotheby’s specialist in contemporary art said: “This astonishingly beautiful painting embodies the profound bond between Lucian and the mother of his two daughters. There is arguably no other portrait by Freud that is more gripping, more tender and more laden with such emotional depth.”

In a statement released by the auction house, Bella Freud said of the image of her mother: “It must have been a very happy time in her life, being pregnant with the man she loved and him wanting her to be there and paint her. I think he was undoubtedly the love of her life.”

"Hideous Kinky" After separating from Freud, Coverley left England with her two daughters to start a new life in Morocco. The story of their bohemian lifestyle in Marrakesh was the subject of Esther Freud's novel Hideous Kinky, which was made into a film with Kate Winslet in the role of Coverley. Coverley and her daughters returned to England. She became a gardener, a writer and a teacher of creative writing. She died, aged 68, just four days after Lucian Freud, in 2011.

In an obituary in the Guardian, Esther Freud wrote: "My mother was an extraordinarily practical and resourceful person, feeding her family from her own garden, teaching herself the Irish drum, taking an Open University degree in English literature and never letting anything stand in the way of her dreams. She took huge pleasure in nature and the last 16 years of her life were spent in the Suffolk countryside, where she made many friends and led an extremely full and varied life, teaching, writing, gardening, dancing and always making time for her children and grandchildren.

“Although she parted from Lucian when her daughters were young, they remained on friendly terms, last visiting him just a few weeks ago, bounding up the stairs to where he lay in bed, never imagining that she would outlive him by only four days.

“She died two weeks after walking into Ipswich hospital, where she was diagnosed with cancer.The day before, although not feeling her usual vibrant self, she had been at Rumburgh drum camp, in Suffolk, attending an Egyptian dance workshop and playing the bodhrán.”

Portrait of Esther By coincidence, the day after the Sotheby's sale, a portrait of Esther Freud, aged 20, by her father will be offered at Christie's London Post-War and Contemporary Evening Auction on Thursday, February 11th. Head of Esther has a top estimate of £3.5 million.

The highest price paid to date for a Freud painting was achieved last year when Christie's sold his female nude painting Benefits Supervisor Resting – featuring "Big Sue" Tilley – a local government worker from London – for $56.2 million (€51.5 million).

After Freud died in 2011, his estate was valued at £42 million, after payment of taxes and debts. But he left the money in a secret trust and it is not known if – or how much – each of his 14 children will receive.

Apart from the two daughters he had with Coverley, Freud had two children with his first wife, Kathleen “Kitty” Epstein; four with Susie Boyt, who had been his pupil at Slade art school; four with Katherine McAdam, who died in 1998; one with the Hon Jacquetta Jean Frederica Lampson, Countess of St Germans, and one with Celia Paul, an artist.