The financier married Cressida's mother Lady Mary Gaye Curzon in 1994, two years after they got together. The couple split in 2000, when Cressida was 11.
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Mr Shaw, a former merchant banker, was a said to be a strong presence in Cressida's childhood life.
Officers were called on Friday to Mr Shaw's rented home in The Close by Salisbury Cathedral after he was found by his housekeeper. A post mortem is to be carried out but Wiltshire police said Monday night there were no suspicious circumstances.
The former merchant banker, who celebrated his 76th birthday on New Year's Day, was a well-known figure on London's affluent party scene in the 1990s, and famous for his lavish soirees.
He had faced health issues in recent years, and was reportedly on medication for kidney problems. Friends told the Daily Mail that he had been told two years ago that he may have as little as 18 months left to live.
The father-of-three was described as "unique" by his long-term friend, PR boss David Wynne-Morgan.
During his marriage to Cressida's mother, the couple lived at the National Trust mansion Hinton Ampner in Hampshire.