As a format, Who Do You Think You Are? (BBC One) appears to have an endless supply of steam. Now in its 16th series, it manages to spin yarns about the long-dead relatives of celebrities that are as compelling as ever.

Part of its appeal lies in its ability to overturn expectations so reliably: uh-oh, you think at the beginning of every episode, this one might be really boring. It never is.

The Harry Potter star Daniel Radcliffe is the first of the new crop of celebrities to get the treatment. He admits to knowing little about his ancestors – he can’t recall his great-grandfather’s name. “I want to say Phil, but that’s not right,“ he says. “This is very embarrassing.” He does remember, however, that this great-grandfather had killed himself.

Radcliffe is in possession of a photo album and a family tree drawn by his Granny Pat just before he was born (he is listed as “bump”). From this, Radcliffe learns that his great-grandfather on his mother’s side was called Samuel; that he was one of nine siblings – the first of them to be born in England; and that his surname, Gershon, was later anglicised to Gresham.

It also turns out that Radcliffe has a living relative he doesn’t know about – also descended from his great-great-grandparents – living in north London. It must have been more of a surprise for Louis Gershon to find out he was related to Harry Potter, but he kept calm all the same.

Louis produces a large photograph of their common forebear – the original Louis Gershon – to whom Radcliffe bears a striking resemblance. “That’s where I get the eyebrows from,” he says.

The original Louis, born in Germany, had spent a number of years in South Africa, where most of his children were born. “He was something in diamonds,” says present-day Louis, “and that’s what was going on out there.” But the census showed that, by 1901, original Louis had relocated to London and set up a jewellery business in Hatton Garden.

By 1930, Samuel (Radcliffe’s great-grandfather) had taken over the business with his brother, got married to Radcliffe’s great-grandmother Raie, and moved to Southend-on-Sea. We already know that his story won’t end well, but the strangest twist is yet to come.

In 1936, the Gershon jewellery business was burgled – the equivalent of £250,000 in today’s money was taken – but the police declined to pursue an investigation. It was their contention that the heist was bogus, the basis for a fraudulent insurance claim. The police contended that the Gershons had form: two very similar burglaries had been perpetrated in the preceding decade, followed by disputes with insurers.

The family also faced prejudice. An informant’s letter, tracked down by one of the programme’s investigators, reminded the police that Samuel was “a Jew, and that Jews are so frequently responsible for the bringing down of their own business premises, and thefts (so-called) committed in their offices.”

“There’s a lot to dig into in that one sentence,” says Radcliffe, visibly stricken by the language. Samuel killed himself five months later. Within weeks, his wife had legally changed her name.

With every episode of Who Do You Think You Are?, there is, as Radcliffe puts it, a lot to dig into. And this is just the half of it – the rest of the episode concerned Radcliffe’s father’s line, Northern Ireland and four brothers who served in the first world war.

Radcliffe makes for an amiable, self-effacing and even-handed conduit, clearly moved by what he discovers, but not gripped by the need to get emotional on behalf of people he never met. Above all, he shows a lot of patience with a format that can sometimes seem like a forced treasure hunt: you must go to Southend, where you will find a historian in a cafe; he, in turn, will send you straight back to Hatton Garden. The locations aren’t necessarily evocative enough to warrant all the travel.

As ever, it is the documents themselves that bring these stories to life: business directories, marriage certificates, witness statements – even, in this case, a suicide note. Names and dates diligently recorded in loopy pencil and faded ink, mountains of pages stored in defiance of the great human business of forgetting – it is all out there somewhere, waiting, and that is why Who Do You Think You Are? will never get old.