Prince Frederik poses for solo Christmas picture as Princess Mary jets off to Australia

Genoveva Casanova, the Mexican socialite, said she "categorically" denies any suggestion she was romantically involved with Frederik after they were photographed together in Madrid.

The Danish Royal Family has not yet commented on any of the allegations.

In the meantime, the Danish royal palace shared a festive solo picture of Crown Prince Frederik lighting candles for Advent.

His wife, Crown Princess Mary, was instead pictured at Sydney airport with the couple's 12-year-old twins Prince Vincent and Princess Josephine.

Mary was born in Hobart, but she married the future King of Denmark in 2004.

The Danish magazine Billed Bladet previously reported that Mary would travel to Australia for the festive period to visit her family.

According to the publication, she will later be joined by her husband and their 16-year-old daughter, Princess Isabella.

Frederik and Mary's eldest child, Prince Christian, 18, will remain in Denmark for studying purposes.

Christian, who is second-in-line to the Danish throne, is in the final year of his secondary education at Ordrup Gymnasium.

Mary was born to Scottish parents, John Donaldson and Henrietta, the latter of whom died in 1997.

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The future Queen of Denmark met Frederik at the Slip Inn pub in Sydney during the 2000 Summer Olympics.

However, Mary did not know that Frederik was a member of the Danish Royal Family.

In a 2005 interview, she said: "The first time we met we shook hands, I didn't know he was the Prince of Denmark.

"Half an hour later someone came up to me and said: 'Do you know who these people are'?"