Harvey was born on 7 August 1969 in Hammersmith, London to the actor Laurence Harvey and fashion model Paulene Stone. Laurence Harvey was still married to Joan Cohn until 1972; he married Stone shortly after divorcing Cohn. After Laurence Harvey died of cancer in 1973, Stone raised Domino in Belgravia, a very affluent area of London. As a girl, Harvey was a tomboy and enjoyed playing with action figures. She later recalled that she studied martial arts and frequently fought other children. She attended four boarding schools, including Dartington Hall and Frensham Heights, and was expelled from some of them.
