Kate, Duchess of Cambridge, heads to the Caribbean with her family Kate, Duchess of Cambridge, arrives to attend a Christmas Service on the grounds of Sandringham Estate, the Queen's Norfolk retreat, England, Dec. 25, 2011. (CBS) Kate, Duchess of Cambridge, has reportedly left rainy London for a tropical vacation with her parents, Michael and Carole Middleton, and her sister, Pippa. Pictures: Kate, Duchess of Cambridge Pictures: Prince William and Kate Passengers were surprised to see the Middleton family in the first class section aboard the British Airways flight from London's Gatwick Airport to St. Lucia, where they are said to fly to the private isle of Mustique, according to People. A photographer's blog adds that Kate and Pippa's brother, James Middleton, was also on the flight. The Caribbean island is frequented by celebrities such as Mick Jagger, Queen Elizabeth's late sister Princess Margaret and Prince William and Kate. William, who a search and rescue helicopter pilot in the Royal Air Force, is believed not to be with the Kate's family - People reports that he'll be spending his week at the RAF base in Anglesey, Wales. The Palace had no comment on the Middletons' vacation.