Markham married actor Corin Redgrave in Wandsworth, London, in 1985. The couple have two sons, Harvey (born 1979) and Arden (born 1983). Markham and Redgrave appeared together twice on screen: first in Lynda La Plante's "Trial and Retribution" (2000) as a judge and barrister, respectively; and later in the BBC's "Waking The Dead" (episode "Special Relationship: Part 1") as lovers suspected of the murder of a government advisor. 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. Her sisters are the actress Petra Markham; the poet and dramatist Jehane Markham, widow of actor Roger Lloyd-Pack; and Sonia. In April 2020, she appeared in an episode of the BBC soap opera "Doctors" as Grace Wilson.