Fake or Fortune? answers a £500,000 question: is this a genuine Lucian Freud?

“We got in an actual tug of war with the picture,” says Turner, now 56. “Dickie wouldn’t let go of it until I agreed to do as he said.”

Turner had just entered one of the British art world’s bitterest feuds. Beginning in a Suffolk art school in 1939, and rumbling on past Freud’s death at the age of 88 in 2011, it would involve international art experts, famous auction houses and, eventually, the German-born painter’s family. At its heart was a single question – was the portrait of a man in a black cravat painted by Lucian Freud?

For Turner this is more than an abstract debate about provenance. Freud’s famously fleshy nude, Benefits Supervisor Resting, sold for £35.4 million in New York last year – the highest price that has ever been paid for a painting by a British artist. If the man in the black cravat is by Freud, it will be worth at least £500,000.

Chopping and Wirth-Miller were old men when they gave Turner the remarkable gift. Chopping was a highly regarded illustrator responsible for the original James Bond book covers. Wirth-Miller was a brilliant tutor, but his career as an artist had not been dazzling. Acolytes of Francis Bacon, the two men were life partners and, like Freud, had both studied at the East Anglian School of Painting and Drawing at Hadleigh in Suffolk in the early 1940s.

An oasis of bohemianism in a country facing the rigours of war against Nazi Germany, the school was housed in a ramshackle 16th-century mansion (its first home burned down when Freud fell asleep smoking). It was noted both for wild parties and co-founder Cedric Morris’s commitment to bold, new modes of painting.

Somehow in this chaotic but fiercely creative wartime milieu, where shortages meant canvases were used and reused, Chopping and Wirth-Miller came by the picture. “They told me it came from the barn at the school or they found it in a junk shop,” says Turner. “There was also a red herring it was stolen at an art fair.”

Turner still can’t pinpoint a specific incident that led to the enmity between Freud and Wirth-Miller, but its fierceness is beyond doubt. As late as 2003, Wirth-Miller – who also died in 2011 – was writing lists of “reasons I hate Lucian Freud”. “There was jealousy,” says Turner. “Freud was always praised as this precocious juvenile talent at Hadleigh and Denis wasn’t.”

Freud, who would leave an estate worth just under £100 million on his death, was one of the most distinctive portraitists of the 20th century, and this early work – which he denied was wholly his – hints at what lies ahead. The sitter has exaggerated features, his chin is lopsided, and the eyes are small and piercing. In short, it shouts Lucian Freud.

Could it really be that his hatred for Wirth-Miller – a man he called “Worst-Miller” – was so strong that he would deny his own work? Was it distaste for a work he thought not good enough? After all, Freud regularly destroyed his own canvases. Or was the painting actually a fake?

Finding out has been a baffling experience for Turner. For more than 20 years, auction houses and experts have told him he owns a genuine Freud, only for them all to change their minds.

“One lady slammed the phone down on me after saying it’s a fake. Her words before were this was the most exciting find that she had ever seen.” In 1983, Christies of London confirmed it was a Freud, only – after talking to Freud himself – to change their mind.

In the decades that followed his time at Hadleigh, Freud became, alongside his sometime friend and longtime rival Francis Bacon, the major figure in the London art world. His reputation was immense – in 2001, the Queen sat for him. Few people would risk their careers by disagreeing with him.

“At one point I suspected Freud was trying to stop me, but I told myself: why would Freud be bothered with me?” says Turner. “Now I’ve changed my mind. I was a thorn in his side. I was continuing Dickie and Denis’ devilment.”

Freud had a reputation for flying into rages. “Sometimes my requests didn’t get as far as Freud because people didn’t want to anger him,” says Turner.

Freud’s daughter was afraid of his temper. In 2006, Turner took the painting to the novelist Rose Boyt (one of 14 children Freud acknowledged as his own), hoping she could get him to give the definitive answer. But Boyt now admits she didn’t show the canvas to her father.

“I didn’t want to because he would probably put his fist through it,” she tells Fiona Bruce on this week’s episode of Fake or Fortune?. "He hated the intrusion of people asking: did you do this or not? I thought if he hadn’t identified it in the normal course of things, that meant he didn’t want to because it was stolen, it wasn’t by him or he hated it.”

Now, thanks to Fake or Fortune?’s formidable line-up of art experts and scientists, the matter can finally be settled. Turner admits he has grown to like the mystery of owning a painting that might or might not be by Lucian Freud.

If it is genuine, will he sell it? “I think so. Then I’d have fulfilled my pledge. It wasn’t about the money for Dickie and Denis. It was a matter of honour. For them, it was about the feud.”

Fake or Fortune? returns tonight, 8pm BBC1