Cooling Castle was the home of George Brooke, 9th Baron Cobham, who was actually Wyatt's maternal uncle. Cobham had withdrawn to his castle after the Crown's forces, under the leadership of Thomas Howard, 3rd Duke of Norfolk, had mutinied and dispersed. According to C S Knighton's Oxford Dictionary of National Biography article on Cobham, Cobham claimed that he had fought valiantly against the rebels for seven hours before surrendering to them, but Knighton points out that his resistance was actually a "pretence" and Cobham joined the rebels willingly. Things were looking good for Wyatt and his men, who then marched on to London.
Picture: Gatehouse of Cooling Castle, Kent, Luke McKernan, Wikipedia.