Beaumont began her career as an actress, before moving to theatre production and stage management. In 1964, she was hired as an editor for the BBC. She transitioned in the company to directing and production management, before leaving the company to pursue film production. In 1971, she made her directorial debut with the horror films The Johnstown Monster and Crucible of Horror. From 1973 to 1980, she worked for Thames Television where she directed daytime television programs.
In 1980, Beaumont produced and directed the horror film The Godsend. After its American release, Beaumont was able to secure a meeting with American television producer Aaron Spelling. Following the meeting, she moved to America and began a decades-long working relationship with Spelling, who hired her to direct shows such as Vega$, Hart to Hart, Glitter, and Beverly Hills, 90210. While working with Spelling on Dynasty, she recommended that he cast her friend Joan Collins as Alexis Colby.