“Got to watch my weight. Because I’m on the telly, you see.” Gregg Wallace – of MasterChef fame – laughs and shrugs. We are sitting in his eponymous south London restaurant, where he’s just had lunch. “I’m working out the calories of what I’ve just eaten. Gotta keep to 2,000 calories a day. On MasterChef, I reckon each tasting is about 50 calories per mouthful.”

He says he goes to the gym three times a day. Then he tells me he has spreadsheets accounting for every single one of his enterprises (which include two restaurants, a small fruit-and-veg business, a farm, plus all the telly stuff). He knows exactly what his money is doing at any single moment of the day. He understands his name, and his fame. He is a proudly self-made man with a keen understanding of his own graft and achievements.

“My fear of poverty is slowly dwindling,” says Wallace, 47, who left school at 14 with very little and now has rather a lot. “I don’t believe in fate. But I was acutely aware that I had less than everyone else. And that left a mark on me.”

A self-confessed amateur historian with a burning family solidarity, perhaps piqued by the devastating teenage discovery that his father was his mother’s long-term boyfriend, not his dad (who was at that point divorcing his mum), it was inconceivable that when Who Do You Think You Are? came calling, Wallace would send the programme-makers away.

Of course, he hoped that the show would uncover something noble, dashing, enterprising. Perhaps, he thought, he might discover that his unexpected father had relations who figured importantly in the Napoleonic wars or the Russian Revolution. He certainly never envisaged the show would bring him to a sense of shame. Or reduce him to tears…

Actually, the show does not consider his wedlock-liberated parentage. Instead, this episode traces the fate of Gregg’s maternal great-grandfather, one Henry Springett, a chap who appears before us in monochrome, wearing a sailor suit.

Not a dashing Captain Springett, but a grimy stoker who went to sea in a steam-powered decoy boat during the First World War. Deliberately concealed as a merchant ship in order to foil, and destroy, U-boats, the decoy boat was one of the unsung heroes of the Navy effort. And the stokers were the unsung heroes of the boat itself, shovelling tons of coal into its furnaces all day and night to keep it going.

“Living in that terrific heat, with the fear that you might be blown up at any time” ... Wallace shudders at the imagined picture. That was the least of it, however; outside the war, Wallace finds that Springett is dogged by death, bereavement and disaster. “He suffers more than any human being should endure,” he says, shaking his head.

Springett’s uncovered history devastates Wallace. “Yes, I cried in the show. I did feel a connection with these people.” Celebrity on-camera tears are often vaguely suspect; here, however, Wallace dares the viewer to remain dry-eyed. “Anyone human would be moved.”

Emily Springett, Henry’s first wife (pictured left with her husband and son, Wilfred), doesn’t fare much better; uncovering the story of her mother Selina (Wallace’s great-great-grandmother) provides the darkest moments in the documentary, since it introduces the spectres of mental illness and the Victorian lunatic asylum. To Wallace, this story is a ghastly, almost taboo tale.

“As someone who is trying to control the fortunes of himself, his family, and makes strides to make sure everyone close to him is looked after, the notion of mental illness terrifies me,” he says, shaking his head. “I felt a sense of shame about Selina. I had hoped that she would been... a person of note, a person to contend with. Instead, she had a defect.”

This is definitely not the terrain of mushrooms, or innovative avocado starters. It’s primetime, but not as Wallace knows and likes it; indeed, he admits that filming Who Do You Think You Are? invited him to wander wholly out of his comfort zone. “You just don’t expect tragedy round the corner. And it is a dreadful thing to say, but I am ashamed of mental illness. I felt it might reflect on me, somehow.”

If he believes this, then his lack of self-censorship is remarkable, but Wallace – who says all he wants to do in life is “make more money” – is nothing if not candid. He believes education is inimically opposed to entrepreneurism, although he’s proud that his 18-year-old son got into the local grammar school near their Kent home. His daughter, 15, is being educated privately. “She’s very posh. But she looks like me in a frock, poor love.” Wallace is bringing them up on his own, after a custody battle with his second wife.

I quiz him about his very public and recent divorce from his third wife, a biology teacher from Cumbria 17 years his junior, whom he met three years ago when she asked him a question about celery on Twitter.

“She is tall, beautiful and young,” he says dreamily. “And very bright. I thought we had a long future together. I got that badly wrong!” So what happened? “Well, we had a row. And she suddenly said ‘I don’t want to do this any more’. I said ‘No?’ and she said ‘Yes!’” Are they still on speaking terms? Of course. “The day after it went public, she tweeted that I was a wonderful man.” Wallace sighs, clearly undiminished by this romantic hiccup… “I love Twitter.”

This episode of Who Do You Think You Are? Is a perfect example of why the show is up for an Emmy award next month. Not only does it gently nudge primetime viewers towards understanding a hitherto unheralded social hinterland – in this case, child mortality, the Victorian asylum and the heroic work of wartime decoy boats – but it does what no regular chat show can: strip celebrities of their fawning pretensions. The show craftily reminds us – and them – how extremely human they are.

For Wallace, a man who believes wholeheartedly in the power of his own graft, stepping back into his family’s past means he must acknowledge that in some lives, hard work is not enough and does not necessarily result in happiness, peace and riches. It just doesn’t.

Gregg appears in tonight's episode of Who Do You Think You Are - 9:00pm, BBC1