The self-appointed queen of hearts had found her king.
As with the first time she met Prince Charles, when he was mourning the loss of his great-uncle, Lord "Dickie" Mountbatten, their fleeting meeting in September 1995 brought out her strong mothering instincts.
Shortly afterwards, this unlikely couple embarked on what would be Diana's last love affair. Their first date was to Stratford-upon-Avon to visit his aunt and uncle, and to pick up some books. "I did not think for one minute that she would say yes, but I asked her to come with me," Khan later recalled. "After this, our friendship turned into a relationship."
Their intense but largely secret two-year romance is now the subject of a new film by the director Oliver Hirschbiegel, Diana.
Naomi Watts plays the love-struck Princess, while the rakishly handsome Naveen Andrews, star of the television series Lost, is the publicity-shy doctor.
The film - the first to deal directly with the last two years of her life - is the latest example of Hollywood's recent love affair with all things royal (think Peter Morgan's brilliantly observed 2006 film The Queen, and 2010's The King's Speech).
In the past, films about Diana have been low-budget, made-for-television affairs that have had scant critical recognition. Given the tragic drama of her life, it is surprising that so few have been tempted to interpret her story.
The movie has propelled Diana back on to the cover of Vanity Fair - the fifth time since her death in August 1997. Her surgeon boyfriend also, reluctantly, returns to the limelight.
This is in contrast with the suffocating secrecy surrounding their affair. They spent their time either in Kensington Palace, where Diana lived alone, or in Khan's tiny Chelsea flat, where she would perform housewifely duties for the doctor, who worked 90-hour weeks.
Diana, then 35, frequently wore a wig and spectacles as a disguise, and once climbed out of a ground-floor window when she visited him at Harefield Hospital in West London to avoid discovery. At other times, she risked all to please the man whom she described as having "dark-brown velvet eyes that you could just sink into".
Shortly after her birthday in July 1996, the Princess apparently met her lover wearing a fur coat, a pair of sapphire-and-diamond earrings - and nothing more.
As with her other relationships, Diana threw herself into his life and interests. When she visited Pakistan on a humanitarian mission in 1996, for instance, she made a point of visiting his parents for tea. She even studied the medical textbook, Gray's Anatomy, so that she could more clearly understand his work.
Her romance coincided with a time when her life was beginning to make sense. She was in discussions with Tony Blair, then Leader of the Opposition, about becoming a roving ambassador; her divorce was finalised on July 4, 1996; and she had a new sense of purpose, symbolised by her decision to sell her gowns at a charity auction in New York.
After meeting Khan's parents, Diana was talking about marriage, children and a new life together in Australia, South Africa or Pakistan. She kept his picture by her bedside, read the Koran each night and introduced Khan to her children.
As she dreamt of becoming plain Mrs Khan, she talked, too, of having a "beautiful brown daughter" whom she would call Allegra, a name suggested by her friend Annabel Goldsmith. She believed that she and Khan could open hospitals for children with heart conditions or hospices on an international scale. "She felt that Hasnat and she could change the world," recalls Toffolo.
Jemima Khan, the socialite, told Vanity Fair that one reason they became friends was her own marriage to Imran Khan, the Pakistani cricketer, now a politician.
"Diana was madly in love with Hasnat Khan [a distant cousin from the traditional Pashtun tribe] and wanted to marry him, even if that meant living in Pakistan," she said.
While the prospect of making a new life with him was a tantalising vision, her single-minded focus was unnerving for the unassuming surgeon. She was intense and obsessive, and her neediness was as demanding as it was compulsive.
The Princess would bombard Khan with texts and calls while he was on duty.
"She was besotted with him, and I think his rather reserved manner made it worse," recalls Simone Simmons, a spiritualist friend.
She would follow him on his rounds and watched him perform operations, on one occasion allowing herself to be filmed in the operating theatre. This led to widespread ridicule from the media, who were baffled by her behaviour.
As the man she described as "Mr Wonderful" absorbed the implications of life in the spotlight, he started to have serious doubts, especially when the press began contacting former girlfriends and professors from his medical school.
Debbie Frank, her friend and astrologer, recalls: "He wasn't at all interested in being a celebrity and would get annoyed if things came out in the press about them, and he would blame her."
While Khan found no allure in the Princess as a celebrity, the altruistic, caring woman who was unafraid to take on difficult causes was quite another matter. This was the tension at the heart of their relationship, the conflict between her public persona and the private princess.
It was becoming clear that Khan felt constrained by the curse of celebrity, the conflicting demands of the Princess and his career, and by their cultural and religious divide.
More than that, he had a fear of commitment, having already been engaged twice and calling off the nuptials at a late stage. (His eventual marriage in 2006 lasted barely 18 months.) "Everyone knew she wanted to marry him," Khan's mother, Nahid, told Pakistan's Daily Times, "but he felt that a marriage would be impossible."
Ultimately, it was the other two men in her life, William and Harry, who became the biggest stumbling block. Khan realised that if they married, they would have to live in Pakistan to have any chance of a normal life together. There was no way the Queen or Prince Charles would have allowed the heir to the throne to be raised abroad.
Khan said last year: "She couldn't have lived in Pakistan at that time - her children were too young [William was 14 and Harry 12]. She couldn't live in two places at the same time, spending a month here or a week there."
They began to drift apart, friends saying that the relationship ended around the summer of 1997. He later recalled: "I think mainly the problem was that even after two years, the relationship wasn't leading to a meaningful progression or conclusion, and that was the main stress on both of us. Everyone wants a relationship to be going somewhere."
Just weeks before her death, Khan met the Princess for the final time at Battersea Park in South London. She said her final farewells. "It was not at all happy," Khan says, with typical understatement, adding: "She was not her normal self." He suspected that she was now with Dodi Fayed.
Some of her friends, such as Simmons and Rosa Monckton, then head of Tiffany & Co, the jewellers, believe that her subsequent courtship of Dodi was a deliberate move to make Khan jealous and encourage him to change his mind about living in Pakistan.
During that last summer she looked sleek and glamorous, posing on the deck of the Fayeds' private yacht or diving into the Mediterranean in a sexy one-piece bathing suit. Her publicity-seeking behaviour was, say her girlfriends, targeted at just one man: Hasnat Khan.
The Princess was still on the doctor's mind, too; he tried telephoning her on August 31, 1997, the night she died, not knowing that she had changed her number.
Of course, we will never know her real motives. It is part of the mystery that remains Diana. Certainly her romance with Khan was highly unusual, although she had long since thrown away the handbook on how to be a conventional princess.
As for Khan, he now works as a heart surgeon at a private clinic in Basildon, Essex, while quietly building a charitable cardiology unit in Pakistan. The 1 million ($1.94 million) unit is in the town of Badlote, near his family home. His aim is to provide free care for poor children in this rural region, something the Princess and the doctor talked of nearly two decades ago.
Diana would have approved.
• Andrew Morton's account of the Princess's last years, Diana: In Pursuit of Love is published next month.
