Castaway (1986)

Middle-aged Gerald Kingsland advertises in a London paper for a female companion to spend a year with him on a desert island. The young Lucy Irvine takes a chance on contacting him and after a couple of meetings they decide to go ahead. Once on the island things prove a lot less idyllic than in the movies, and gradually it becomes clear that it is Lucy who has the desire and the strength to try and see the year through.