Beacham's initial goal was to teach dance movement to deaf children, but she began a career in modelling and then began acting in television. Her first screen role was in the BBC series "The Queen's Traitor" in 1967, in which she played Mary, Queen of Scots. During an interview, thinking Barnet sounded uninteresting, she told a reporter from the "Northern Echo" she was born in Casablanca, where her favourite Bogart/Bergman film was set. After many further guest appearances in television series such as "The Saint", "Callan", and "UFO", Beacham's first film roles were in "The Games" directed by Michael Winner, and "Tam Lin" directed by Roddy McDowall, both released in 1970. She would work with Winner again in 1971's "The Nightcomers", in which she starred opposite Marlon Brando. Beacham appeared nude in one scene, during the filming of which Brando wore Y-fronts and wellington boots under the bed clothes to ensure Winner did not film anything lower than was necessary. Horror would be a genre that Beacham appeared in often during this period, and she was subsequently cast as Jessica Van Helsing in Hammer's "Dracula A.D. 1972" alongside Peter Cushing.