The British prime minister and his family have enjoyed five holidays at the Italian aristocrat's home outside the town of San Gimignano since 1998, and perhaps what keeps Blair coming back are the subtle yet strangely familiar smiles radiating across the Strozzi dinner table from the prince's daughters, Natalia and Irene.

Because now, an Italian genealogy expert, Domenico Savini, has revealed that the Strozzi family descends directly from Lisa Gherardini, otherwise known as the Mona Lisa.

"It's a matter of great emotion and great pride to learn that we are descended from La Gioconda, " said Natalia Strozzi, 30, an actress. The subject of Leonardo's most famous painting is known as 'La Gioconda' in Italy, a pun on her husband's name (Francesco del Giocondo) and her "gioconda" (jocund) expression. "We had a vague knowledge of this family story, but the fact that it's been documented proves that it is true, which makes us take it more seriously."

And what about that celebrated smile? "Yes, " she continued, "once in a while a smile like that flits across our father's face, and that's the most convincing proof there is."

Italian researchers have been closing in on the Mona Lisa in recent weeks. Not only have her descendants (by the female line) been identified in the Strozzi family, but one of the most tenacious Leonardo researchers, Giuseppe Pallanti, claims to have unearthed church documents proving where she lived and died.

Pallanti recently told a packed press conference in Florence that, after sifting through thousands of archive documents, he had discovered that the remains of Lisa Gherardini are buried in the dilapidated ruins of a convent in the centre of Florence, Convento Sant'Orsola.

Signora Gherardini moved into the convent, where her daughter was a nun, when her own health began to fail after her husband's death in 1538.

She died four years later, on 15 July, 1542, at the age of 63. It was 39 years after her portrait was painted.

The convent on Via Stufa was round the corner from her family home, as well as that of Leonardo himself. Her father had been a close friend of Leonardo, and Pallanti believes that the background to the painting was the view from Santa Maria Novella church, which is in the same neighbourhood.

It did not take long for Pallanti's researches to be politely rubbished: Mona Lisa studies is an acrimonious field, and claimants to the title of Leonardo's true model for the picture range from the artist himself or one of his putative boyfriends to a baffling array of prostitutes, courtesans and society ladies.

While congratulating Pallanti on his discoveries, Leonardo scholar Carlo Pedretti pointed out that what is still missing is "documentary proof to connect Lisa Gherardini to the woman in the Gioconda portrait." But definitive identification may not be far away. Maurizio Seracini, famed for his forensic work on great paintings, has offered to begin rooting round under the convent for Lisa Gherardini's remains.

If they were found, it would not be beyond modern technology to reconstruct her appearance and settle the question of whether she was the true Mona Lisa once and for all. At the same time, DNA tests could determine whether the Strozzi girls really have something to smile about.