Possessing an early ambition to become a professional tennis player, she spent two years at a tennis academy in Florida. Richardson then turned to acting. In 1985, she portrayed, by flashbacks, the younger version of the leading character played by her mother in the film "Wetherby". After a leading role in Peter Greenaway's cult success "Drowning by Numbers" (1988), her first major role in front of a mass audience was as Joanna Farley in a 1989 television episode of "Poirot", based on Agatha Christie's detective series. In a 1989 episode of "Jim Henson's The Storyteller", she was cast as a princess. She portrayed a teacher on the verge of a nervous breakdown in the 1989 Channel 4 serial "Behaving Badly" and fictional Finnish Princess Anna (with "a voice like a tuba") in the 1991 screen comedy "King Ralph".