The private island where Kate was photographed

The pictures, which have been condemned by St James's Palace, reportedly show the Duchess of Cambridge wearing a bikini and strolling on a beach on the private island of Mustique with her husband.

The small Caribbean island, a former sugar plantation that is part of St Vincent and the Grenadines, in the West Indies, has long been a haven for the rich and famous.

File picture of the private island of Mustique in the West Indies. Credit: PA Wire

In 1958 by Colin Tennant, the 3rd Baron Glenconner, bought the 1,400-acre island for 67,500 dollars (£43,000) to create a luxurious private retreat.

Three years later he gave a 10-acre plot as a wedding gift to Princess Margaret, on which she built a magnificent villa, Les Jolies Eaux.

Mustique is now owned by the Mustique Company, a group of shareholder home owners from 17 countries, which preserves and runs the island.

It has 100 private residences, 74 of which are available for rent, the 17-room Cotton House boutique hotel and a five-bedroom guesthouse, according to the Mustique island website.

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This Morning Kate mag apology

ITV's This Morning has said it is "very sorry" after accidentally showing an uncensored cover of the Italian magazine that pictured a pregnant Duchess of Cambridge in a bikini on holiday on the private Caribbean island of Mustique.