As a child, Mills appeared as an extra in various films, including a role as Freda's 11-week-old baby in the 1942 film "In Which We Serve", starring her father. Her first major role came in 1958, when she was 16, in the Peter Shaffer play "Five Finger Exercise", as "Pamela Harrington". The show ran one year in London, and then moved to the Music Box Theatre on Broadway. In 1960, Mills was nominated for a Tony Award as "Best Featured Actress" for her performance as Pamela.