She discovered a number of talents who became big names, including Richard Burton, later one of Rye's lodgers.
Nigel Hawthorne said of her: "How daunting it was to hear her voice coming from a darkened auditorium during auditions."
Her theatrical credits as director included Private Lives, Edward, My Son and The Little Hut.
Her marriages to the actor Roland Culver and Dr John Janvrin were dissolved.
In 1963, with the backing of friends, Rye established a restaurant in Chelsea called Daphne's, which became a celebrity hangout, attracting the likes of Laurence Olivier, David Niven, Alec Guinness and Prince Charles.