HE WAS the original pop idol, a brash entertainer with links to the Mafia. She was the Queen’s wild younger sister, a princess famed for her beauty, whose life tore a blazing path through popular culture.

Now an affectionate handwritten letter from the Princess Margaret to Frank Sinatra has been discovered, inviting Ol’ Blue Eyes to come swing with her at Kensington Palace.

It was March 1971. Sinatra had contacted the Princess from aboard the QE2, as he prepared for a tour in London.

Her two-page reply, dated March 19, bears her distinctive M insignia, reveals her home telephone number, and requests a personal performance of the song Out of this World.

The Princess, who at the time was darling of the gossip columns and regularly voted one of the world’s most beautiful women, could only have been flattered by the lyrics.

In the song, Sinatra who had divorced the actress Mia Farrow three years earlier, would profess his love for her — for not one but two eternites.

The Princess’s own marriage to Lord Snowdon was to end in divorce five years later.

She had known Sinatra for more that ten years. Inviting him to dinner at the palace, she wrote: “Dear Frank, So nice to hear from you from the dear old ship and we would love to dine with you and perhaps it would amuse you to see the ancient dwelling (1690) which we have brought up to date.”

The Princess, who was referring to her apartments at Kensington Palace, gave him her telephone number — the Clarence House switchboard.

“My mother’s house so don’t be put off and think that you have the wrong place. Because the operator will put you through.”

In the letter, which has been acquired by Argyll Etkin, the London auctioneers who specialise in Royal memorabilia, the Princess requests one song. “Please brush up on the Out of This World song for all the fans of that particular music awaiting you,” she wrote. “Yours very sincerely, Margaret.”

Ian Shapiro, the joint managing director of Argyll Etkin, said that the letter was fascinating. “She was not a prolific letter writer, which is what makes this so interesting. She signed letters to the family Margot, and to friends Margaret.”

The auction house acquired the letter on Kensington Palace headed notepaper from a private customer. It is valued at about £1,500.

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