[6] She made her film debut in the 1961 low-budget crime caper 20,000 Eyes, and guest-starred in television series such as Leave It to Beaver, The Untouchables, Perry Mason and The Wide Country.

Parkins was involved in two of the most highly publicized projects of the 1960s, the ABC primetime serial Peyton Place, and the film adaptation of Jacqueline Susann's best-selling novel, Valley of the Dolls.

After visiting London in 1968 to be a bridesmaid in the wedding of Valley of the Dolls co-star Sharon Tate and director Roman Polanski,[8] Parkins moved to England, where she starred in several productions, including Puppet on a Chain (1970), The Mephisto Waltz (1971), and Shout at the Devil (1976), Parkins said she moved to London because it was relaxed and simple, and she loved its traditions.

In the 1970s and 1980s, Parkins appeared on American television in series that included Jennie: Lady Randolph Churchill, Captains and the Kings and The Testimony of Two Men, Fantasy Island, The Love Boat, Hotel, and Vega$.

She also appeared in television films, including To Catch a King, in which she portrayed the Duchess of Windsor, and opposite Sharon Stone in Calendar Girl Murders.