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.
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.
More top news
Britain's immigration system is in 'critical condition' according to the chair of the Home Affairs Select Committee.
Showers across Britain will make way for sunshine tomorrow before a milder end to the weekend, though heavy rain will return in the north.
George Clooney appeared in a special Downton Abbey as a host of stars came together to raise money for the ITV charity campaign Text Santa.