Bisset was born in Weybridge, Surrey, England. Her birth name is Winifred Jacqueline Fraser Bisset She is the daughter of Arlette Alexander, a lawyer-turned-housewife, and Max Fraser Bisset, a general practitioner. She was brought up in Reading, Berkshire, where she lived in the suburb of Tilehurst. Her father was Scottish and her mother was of French and English ancestry;