About four years ago the writer Thomas Harding and his daughter Sam were walking around central London. Harding pointed out building after building — landmarks such as the Trocadero, hotels such as the Cumberland and the Strand Palace — which had once belonged to his family’s company, J Lyons and Co.

Lyons was once one of the most famous names in British food, spanning a vast empire which took in hotels, teashops, restaurants, catering, and iconic brands such as Lyons Maid ice cream, Tetley Tea, and ReadyBrek cereal. And yet, its financial collapse and eventual disappearance as a company was painfully rapid in the 1970s, so that Lyons effectively vanished. Harding himself realised he knew almost nothing about his mother’s eclectic and extraordinary family who had built the J Lyons name — but he was determined to find out.

The result is his magnificent book, Legacy, winningly subtitled “One family, a cup of tea, and the company that took on the world”. In its pages we discover the endlessly fascinating lives of the Salmon and Gluckstein families, once primarily Orthodox Jews, and once, indeed, a sort of ring-fenced Jewish cousinhood who mainly married each other.

Harding took on this mountainous project having grown up with very little to do with his mother’s side of the family. He had plumbed the story of his father’s family, the Alexanders, for his best-selling social history, The House by the Lake, about their lives in Berlin; but he scarcely knew the huge network of Salmons and Glucksteins whom he is now happy to call his relations. “I wouldn’t have known them if I had walked past them in the street”, he says.

Now, however, as the chronicler of the J Lyons story, Harding has almost more relations than he could shake a stick at, and he is amused that many of them share the same traits. A standard response which a number have in common is to send back badly cooked food in restaurants — “out of respect for the chef”. It is something which Harding himself does, though he was not aware of its origin.

The family company may be no more, but the family has thrown up a vast number of over-achievers in public life: from Alastair Salmon, head chef to the Lord Mayor of London, to Nigella Lawson — whose mother was Vanessa Salmon — the food writer and presenter. There are journalists such as the social commentator George Monbiot and Reuters’ Felix Salmon, and Nigella’s brother Dominic Lawson. There are “a whole raft of lawyers”, including Fiona Shackleton, the formidable baroness who has represented members of the royal family and Sir Paul McCartney in high-profile divorce cases.

The joke, of course, is that the family company called itself J Lyons at all. Desperate to assimilate into British society, the Salmons and the Glucksteins found themselves a front man in the person of Joe Lyons who was, says Harding, not very smart but was more than happy to be the public face of a growing and successful company. Thus it was Joe Lyons who became Sir Joseph Lyons for services to the catering industry, while the founding architects of the success, Montague (Monte) Gluckstein and his brothers, maintained a more private profile.

To begin with, Harding asked his mother for help. She gave him three names —“all men” — to talk to. The gender is significant because the family was sitting on an enormous secret which paralleled their public success.

This was The Fund, first created in 1873 by Monte Gluckstein and five of his brothers and brothers-in-law. The Fund, open only to male family members aged 23 or older, was an extraordinary financial support. Its rules, passed down orally from generation to generation, stipulated that “once a member, you must contribute all of your earnings to the Fund, even if you do not work for a family business”. All members received a similar wage, drawn from the Fund, a company car and driver, a home, private health insurance and education for the members and their families.

Women were not eligible to be members of the Fund, which caused “great anger”, says Harding, among some of the family members he spoke to. This “community of interests”, a sort of benevolent fund crossed with a lifetime pension, was a family secret.

So although The Fund had been wound up by the time Harding began his research, there was nervousness about revealing its existence. He thinks, also, that there was anxiety about the criss-crossing intermarriage among cousins.

Fortunately for Harding, despite the nervousness of family members about his plan, there was an unexpected bonus. For the Salmons and Glucksteins were obsessive tellers of their own stories, and there were numerous unpublished memoirs on which he was able to draw for Legacy.

They enabled him to untangle the clotted family network, and pick out one leading ancestor per generation to illustrate his story.

And what a story this is: of a shy Hebrew teacher in very early 19th century Germany, Lehmann Gluckstein, who may have faked his own death in order to flee the law. He and his young family arrived in Whitechapel in 1844, sending eldest son Samuel ahead a year before to scout out the opportunities.

The business began with tobacco shops and then moved, gradually, into food and catering. By 1906, as Harding records, J Lyons, as the undisputed king of British catering, was responsible for a mammoth banquet to celebrate the 400th anniversary of the University of Aberdeen, sending massive quantities of food — including 90 turtles, destined to be made into soup — from London Euston to Aberdeen.

The celebration, naturally, was attended by King Edward and Queen Alexandra. By that time the royal family were turning to J Lyons to cater its Buckingham Palace garden parties and the firm also provided the food at Wimbledon tennis championships.

At almost every stage, the Salmons and Glucksteins did well by anticipating the needs of the public. Their modus operandi was to believe that people would say “What a good idea” — and respond accordingly.

So it was J Lyons which was at the forefront of social innovation by beginning the chain of tea-shops, the famed Lyons Corner Houses, with their “Nippy” waitresses, which allowed women to go out and eat in public in comfort and without male chaperones.

It was J Lyons which brought women into the workforce during the First World War, and — astonishingly — produced one-seventh of the bombs dropped by the Allies during the Second World War. It was J Lyons which developed the world’s first business computer.

Alongside these extraordinary developments, which ensured that J Lyons became an integral part of British life, members of the family were struggling with their Jewish identity and how it squared with their longing to be seen as British first. So in 1911 we learn how Monte Gluckstein became one of the founders of the Liberal Jewish Synagogue in St John’s Wood because, as Harding records, he “thought it hypocritical that up and down the country his family’s teashops sold bacon and eggs for breakfast, ham sandwiches for lunch, and pork chops for dinner, yet in their own dining rooms they were adamant about keeping kosher”.

In 1918 we find Isidore Salmon throwing himself into working for the Board of Deputies. Isidore — Harding’s great-grandfather —was to become an MP and was knighted but was not highly regarded by many members of the family.

Throughout the book Harding records the “inside and outside” pressures between being British and being Jewish, and also the irony of J Lyons’ decided advances for women in public, while the family’s Fund and the shape of the company essentially disbarred many of the women from the decision-making process.

It is a fascinating and at times frustrating story, with heroes and villains crowding the pages. At the conclusion of the book Harding, having contacted more than 60 of his new-found relatives, goes to a small and hitherto neglected Jewish cemetery in Hackney where the family founder, Lehmann Gluckstein and his wife Helena, were buried in the 1850s.

Advised that the synagogue responsible for the cemetery was about to make some major repairs, Harding agreed to help fix up some of the dilapidated graves and put up “an interpretative sign” near Lehmann and Helena’s tombstones. His new cousins agreed to help finance the restoration with alacrity and now Harding’s only problem was the wording of the sign.

After much internal struggle, here is what he wrote: “Here lie Helena and Lehmann Gluckstein. Matriarch and patriarch of the family who founded the catering firm J Lyons and the tobacco retailer Salmon and Gluckstein. Whose legacy was: Find a safe place. Love your family and friends. Give back to society. Savour the good things. Tell your story. Pass it on”.

Legacy will be published by William Heinemann on August 29