Christopher Shaw, a 76-year-old retired banker, was married to Cressida's mother, Mary Gaye Curzon, from 1996 to 2000.
UsMagazine.com said Tuesday he was found dead last Friday.
The Mirror reported his body was discovered by his housekeeper shortly after he returned from a vacation in Cuba.
Shaw had been suffering from long-term health problems, including chronic kidney disease, and was told he had 18 months to live, UsMagazine.com said.
The exact cause of his death has not yet been determined; however, the Sun reported it is an apparent suicide from an overdose of pills.