Filming Channel 4's one-off show Miranda Does Christmas, the pair locked lips as part of the show's rowdy Christmas party theme.
There were no modern conveniences – even a camera was a novelty – and the journey to Mustique from England took three days.
"It was like a graveyard," said Tennant, "run down and badly managed – very mouldy." At first Tennant bought the island simply because he liked the beaches and thought it would be a pleasant place to retire.
The island's popularity was assured when, during Princess Margaret's honeymoon visit to Mustique in 1960, Tennant gave her a piece of land as a wedding present.
Later he built her a Georgian-style colonial villa, Les Jolies Eaux.
The show, which is an adaptation of Neil Gaiman and Terry Pratchett’s book of the same name, will be the second adaptation of a Neil Gaiman novel by Amazon, following the success of American Gods earlier this year.