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In some ways, this conscious or unconscious need for family drew her to the quintessential family. Diana harboured a naïve teenage vision of the Queen Mother and the Queen being some kind of maternal guardians, guiding, nurturing and nourishing. This vision soon evaporated.

"From the first day I joined that family, nothing could be done naturally any more," she told Le Monde just before her death in August 1997, articulating the frustrations she felt with the constraints of royal family life.

Another reflection of her desire for family, or at least the shared remembrance of family, was the unlikely friendship she forged towards the end of her life with her stepmother, Raine Spencer. It seemed that Diana wanted to maintain a connection with her late father, Earl Spencer, through the memories of his wife, the woman she once called "Acid" Raine.

"I always thought that one of the reasons she wanted to be friends was because she and I were the only people who could talk about Johnnie together," Raine told me.

Diana enjoyed an uneven relationship with her own family, at different times falling out with her mother, her sisters and her younger brother, Charles (who succeeded his father as the 9th Earl Spencer in 1992, inheriting the family's ancestral seat in Althorp, Northamptonshire). "They were a very volatile family in that you could never be sure which one had fallen out with which other one," recalls her friend Vivienne Parry. "Yet they were close, despite the fact that they constantly had rows, and if an outsider criticised them, it would be seen as an attack on them all."

As a youngster, Diana's own experience with grandparents was somewhat mixed. While her maternal grandmother, Lady Ruth Fermoy, taught her card games, it was her paternal grandmother, Cynthia, Countess Spencer, who was the queen of her heart.

"She was sweet and wonderful and special. Divine, really," Diana told me. The countess was known locally for her visits to the sick and elderly, and was never at a loss for a generous word or gesture. When she died of a brain tumour in 1972, Diana, then 11, was heartbroken. The princess believed, "for a fact", that she watched over her from the spirit world.

Her grandfather, the 7th Earl Spencer, was a different proposition. He was taciturn and irascible to the point of rudeness, and Diana and her brother Charles found visits to Althorp terrifying. Besides the daunting figure of their grandfather, whose iron rule was "no small talk", there was the stately pile itself, with badly lit corridors peopled with portraits of long-dead ancestors. ''For an impressionable child, it was a nightmarish place," recalled Diana's brother.

When she had her own children, Diana smothered them with affection, in her own words "hugging them to death each night". But at the same time as giving William and Harry unconditional love, she made them aware of their future responsibilities.

"Diana said repeatedly that the boys should be fully aware of what was expected of them, but that they should also be allowed to develop as young men," said her bodyguard Ken Wharfe. ''One of her frequent phrases was: 'I do whatever is best for my children.'" The prim tone brooked no argument.

Thus her joy at the birth of her grandson, and of being a part of an extended biological family, would have been unconfined. The birth of a baby always resonated deeply with her. During her frequent private visits to the sick and dying in London hospitals, she always made a point of seeing the newborns in the maternity unit. Their innocent presence confirmed to her the wheel of life.

As much as she adored babies and family, the events of this week would, I believe, have given Diana pause. The fact that she would be overshadowed by the newborn would not rankle. By now, she would have been well used to life as a sideshow in the public's love affair with Catherine Middleton. There would be some amused consolation in the fact that she and Carole Middleton would be hailed as leaders of the new breed of "glammies", glamorous grandmothers whose looks belied their years.

What would touch a maternal nerve, however, is that Diana, like millions of grandmothers before her, would have had to learn the art of restraint. She would be reminded that it is the mother, not grandmother, who knows best. While her enthusiasm for the infant would be overpowering, she would, reluctantly, have to step back and let the primary care-givers, William and Catherine, decide how to bring up baby. Diana would be relegated to the chorus, albeit an important voice.

For all her international sheen of sophistication, the royal glammie would have had to experience the realisation that humility is the price of admission into the Grandmothers' Union.

Even more galling, as the mother of the new father, Diana would not have had quite the same easy access to her grandchild as Carole Middleton. In most families, new mothers tend to lean on their mothers for support – hence the fact that Baby Cambridge will be shuttling back and forth from the family apartment in Kensington Palace to Carole and Michael Middleton's home in Berkshire. Diana might have been left watching from the wings.

She would, though, have had one enduring consolation. As the new infant shares the same Cancer birth sign as the late Princess, the youngster would doubtless share some of her personality traits. One of the first things Diana would have done would be to commission a birth chart by one of her trusted astrologers.

As her one-time astrologer Penny Thornton says: "I suspect that Diana's genetic and psychic imprint will be firmly on that child."

That, I think, would have been Diana's greatest gift of all.