The star, who rose to fame in the 1990s as a hard-partying "It girl", received treatment in 2016 for a non-malignant brain tumour.
The Met Police confirmed a woman in her 40s was found dead at Palmer-Tomkinson's flat in Bramham Gardens, South Kensington, at 13:40 GMT.
Prince Charles, a close friend of the star's family, led tributes and said he was "deeply saddened" by her death.
Palmer-Tomkinson, a former Sunday Times columnist and reality TV star, was a regular on the London party scene in the 1990s and 2000s.
