According to Channel 5 documentary The Royals on Holiday, it was Princess Margaret who first fell in love with the island.
In the documentary, Richard Kay, editor-at-large at the Daily Mail explained: “Colin Tennant offered her a plot of land as a wedding present and she said, ‘Thank you very much, yes I’d like that.’
“They literally marked it out with their feet and Margaret said: ‘Well I’d like a bit more.’ So she sort of kicked the sand a bit further and it got a bit larger and he went along with that.
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“They used to stay up until all hours partying and having fun.
“She wasn’t particularly suited to royal life with all of its rules and regulations and protocols.
“She enjoyed the privilege and the things it afforded her, but those restrictions really were quite damaging to her, I think, and for a large part of her life she wasn’t all that happy in the Royal Family.
“Mustique was that place she could go and let off steam, enjoy everything about life and not have to worry.”
As the documentary states: “They were not just candid photos of Margaret on holiday. These pictures would have major repercussions.”
Ms Joseph explained: “Even though they thought they were away from the cameras, the News of the World managed to grab a photo of her on the beach with Roddy Llewellyn and obviously it went around the world.”
Mr Kay added: “It was that trip to the Caribbean where the wider world found out she was conducting an affair with him.”
“Lots of people were saying is it at all suitable that the Queen’s sister should be carry on like this and it did make things really tricky for a moment,” he said.
Victoria Howard, editor of The Crown Chronicles, said: “To see a royal princess in her swimming costume on the beach but also with a man who was not her husband.
“Rumours had been circulating for a while that maybe Tony and Margaret weren’t all that happy, that things had got a bit bumpy in their marriage, but this seemed to cement those rumours.”
According to the documentary these photographs marked a “pivotal moment in history” for the Monarchy.
Just three years later Princess Margaret divorced her husband Antony Armstrong Jones.
She was the first senior royal to do so since Henry VIII.