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), High Tide (1980), Outland (1981, as Sean Connery's wife), The Innocent (1985), Wonderland (1999), Esther Kahn (2000), Killing Me Softly (2002) and Franklyn (2008).

They also appeared on stage together in an acclaimed revival of Noël Coward's A Song at Twilight, along with sister-in-law Vanessa Redgrave.

[citation needed] In April 2020, she appeared in an episode of the BBC soap opera Doctors as Grace Wilson.

[5] Markham's memoir of her husband, Our Time of Day: My Life with Corin Redgrave, was published in 2014.