Anneke played Doctor Who companion Polly from 1966 to 1967. Her other television credits include appearances in The Avengers and Strange Report. Acting aside, Anneke has had an extraordinary life. One of her early boyfriends was Daphne du Maurier's son, Kits Browning, but it was Edward Fox who was her first love. At 17 she began a relationship with Anthony Newley while working on the TV series The Strange World of Gurney Slade. Later, she married Michael Gough, the distinguished actor who played The Celestial Toymaker in Doctor Who.
During the sixties, Anneke spent much of her time at the famous Troubadour Coffee Shop and The Establishment, and was part of the so-called Chelsea Set, counting among her close friends Peter Cook and Dudley Moore, Sammy Davis Jr, Kenneth More, Sarah Miles, and many more leading lights of the sixties.