^"He disappears." These were the last words I wrote in A Book of Secrets about John Francis Mordaunt, the son of Eve Fairfax.

At the beginning of the 20th century, in her late 20s, Eve had become engaged to Ernest Beckett, a Yorkshire banker and MP. He arranged for her, properly chaperoned, to travel to Paris where the sculptor Auguste Rodin could make a bust of her as a wedding present. But the wedding never took place. It was rumoured Eve and Rodin had a love affair. Certainly an emotional bond grew between them – they continued writing to each other and she went on intermittently sitting for him until just before the first world war – but this was later and unlikely to have been the cause of Beckett's disappearance from her life.

In 1905, following the death of his uncle, the first Lord Grimthorpe, Ernest (whose father had previously died) inherited the baronage. He had gambled away his own fortune, lost his position as a banker and owed a great deal of money. Knowing his uncle, a scholar of locks, clocks and bells (he designed Big Ben), had been wonderfully wealthy, Ernest's creditors gathered round him, demanding to be paid. Unfortunately the first Lord Grimthorpe had also been an aggressive litigant, adding more than 20 contentious codicils to his will, which delayed probate for more than two years. To escape bankruptcy while waiting for his legacy, Ernest sold his properties in England and escaped to Italy where he bought the spectacular Villa Cimbrone at Ravello, overlooking the Gulf of Salerno. He spent much of the next 15 years travelling abroad.

Eve Fairfax, though much admired by many men, never married. Perhaps she was considered "damaged goods"; perhaps she grew embittered after being abandoned by Ernest. Certainly she would not have surrendered her name easily. She was proud of her family, descended from General Lord Fairfax whose parliamentary army defeated Charles I's troops at the Battle of Naseby in 1645. All her life she was "fair of face", but she had no money and was for years supported by wealthy friends.

Many rumours and speculations circulated round this mysterious figure. It was said she had an illegitimate child, but I did not believe this until, helped by the Grimthorpe family, I was given evidence. Early in March 1916, Eve entered a nursing home at 15 Welbeck Street in the west end of London, and on 7 March her son was born. She named him John Francis Mordaunt. It cannot have been an easy experience, giving birth to a first child in wartime at the age of 46. But the Welbeck clinic was an expensive and discreet hospital. Eve and her son were well looked after by the matron there, Clara Nelson Smith, who was present at the birth.

Reaching this point in the story, I looked through the birth, death and marriage files to see if there had been an infant death that year of John Francis Mordaunt. None was recorded. The birth certificate gave no father, but a note from one of Eve's friends to the Grimthorpe family stated that the father had been Désiré Defauw, a Belgian musician who had come to Britain in the war and led the popular Allied Quartet. I could find nothing that connected him to Eve.

I looked into the career of Clara Nelson Smith and found she had been awarded the Royal Victorian Order after a member of the royal family had died in the Welbeck nursing home. The cause of his death was unknown and his will was sealed, creating a precedent for future royal wills. Evidently the matron had been rewarded for her discretion. There could have been no better place to conceal an illegitimate birth. Though Eve was to live until 1978, dying in her 107th year, she made no mention of a son. "He disappears."

But then, 10 months after my book was published, the secret of John Francis Mordaunt's life was revealed. A reader telephoned my publisher and came to see me. She was his daughter – and Eve Fairfax's granddaughter (she had not known this until she read my book). Her father, she told me, had been brought up, a solitary child, at the Welbeck nursing home, looked after by Clara Nelson Smith. Eve's friends must have paid for his upkeep and later sent him to the Merchant Taylors' independent school, after which he studied at Guy's hospital and University College hospital, where he taught dentistry before joining a private practice. In the second world war he joined the RAF and went out to Kenya. He got his wings, flew, returned to England and in 1942 married a girl whose family was returning from India. They had two daughters, Joanna being the younger.

But John Francis Mordaunt seemed destined for tragedy. In 1964 he, his wife and their elder daughter died in a plane crash at Innsbruck. They were going skiing, but Joanna, then 14, did not go with them as she was in training at the Royal Ballet School at White Lodge in Richmond Park. She was subsequently brought up by her godfather and went on to be a dancer with the Royal Ballet and English National Ballet, then later a paino teacher.

In 1972 Joanna married Roger Vickers, a distinguished orthopaedic surgeon; they had two daughters and two sons. Despite her successful career and happy family life, the mystery of her father's life and the absence of relatives disturbed her. Who were the Mordaunts? Who were her grandparents? Why had her father grown up in such strange circumstances? She remembers him as being quiet, rather shy, extremely athletic and good at all sport. But he had not seemed to know the answers to these questions, and those who had paid for his upbringing and education did so on condition that no one should reveal who his parents were.

Joanna asked at the Merchant Taylors' school, to her father's university, Guy's hospital and the Welbeck clinic, but got no answers. Encouraged by her children, she asked a friend to help. Margaret Bohn, an amateur genealogist, also drew a blank – until late summer this year when, in a final shot, she typed the name John Francis Mordaunt into her computer again. This time my book appeared on the screen.

Two weeks later Joanna and I met. I was able to put her in contact with one or two people who had helped me and could now help her. There was, for example, Eve's great-niece Serena Sparks and her husband Alexander, who lived in Wiltshire and who owned an enormous volume Lady Diana Manners had given Eve in 1909. This she carried with her for the rest of her long life, insisting the people she met write something in it. So it became a history of her social life, and within it lay the seed of an ingenious idea Joanna had as to who her grandfather might have been if it was not Désiré Defauw.

In Eve's extraordinary leather-bound book, there is a surprising entry by Ernest who, in his late 50s, was visiting Britain to see his daughter who was seriously ill. He wrote in Eve's book a devastating verse from Swinburne's poem "Dolores (Notre-Dame des Sept Douleurs)" ending with the lines: "And marriage & death & division/Make barren our lives." He dates his entry 25 May 1915 and signs it "Grimthorpe". This meeting, Joanna points out, was a little over nine months before John Francis Mordaunt was born. Is it not possible, she asks, that a dozen years or more after their engagement was broken off, Ernest became Eve's hidden lover, Joanna's missing grandfather? A year later, having caught tuberculosis from his daughter, Ernest died. And so in the end it is he who "disappears".