Bexley, who had been with the organisation for four years since joining from Unicef, will not be replaced. Her responsibilities will be assumed by senior press officer Lucinda MacPherson.
The resignation comes at a difficult time for the charity.
Although it succeeded in suing collectibles company Franklin Mint for using Diana’s image following a well-publicised court battle, Franklin Mint counter-sued for malicious prosecution.
The case is due to be decided in November, when a judge gives his verdict on whether it goes to trial.
The fund has been unable to issue grants from its own assets since July 2003, while waiting for further developments in the case.
Bexley said: ‘I will continue to work part-time as a freelance PR and communications consultant while I wait to see what’s round the corner.’