Felicity made her stage debut in these productions, and at the age of nineteen, starred in the film, Shakespeare Wallah (1965), loosely based on her family's real-life experience. On her return to Britain, she found that her film appearance was not a passport to success, and her struggle to build an acting career was long and difficult, partly because of her unusual upbringing. In 1975, she got her big break with the sitcom, The Good Life, which made her a household name. She was particularly popular with male viewers, and was voted "Rear of the Year" for her appearances wearing wellington boots.
After series ended, she starred in several other BBC sitcoms, none of which came anywhere near the success of The Good Life. Despite this, she maintained her popularity.
Felicity's stage career blossomed during the eighties and nineties. Her relationship with playwright Tom Stoppard was both personal and professional. She starred in the first productions of many of his plays; in 1991 Stoppard left his wife to start a relationship with her.