Markham has had a long career in the cinema, television and theatre as an actress. Among her television appearances are roles in "Edward & Mrs. Simpson", "The Life and Times of David Lloyd George", "A Very British Coup", "Van der Valk", "The Line of Beauty", "Minder", "Cracker", "Agatha Christie's Poirot" "(The Double Clue)", "Sherlock Holmes' Wisteria Lodge" and "Mr Selfridge". Her films include "Bunny Lake Is Missing" (1965), "Futtocks End" (1970), François Truffaut's "Two English Girls" (1971), "Operation Daybreak" (1975), "Noroît" (1976), "The Blood of Hussain" (1980), "Outland" (1981, as Sean Connery's wife), "The Innocent" (1985), "Wonderland" (1999), "Esther Kahn" (2000), "Killing Me Softly" (2002) and "Franklyn" (2008).