Born in London into a theatrical family, Nicholls began acting as a child (billed under her given name, Sarah Nicholls) alongside her parents, actors Faith Kent and Anthony Nicholls. In her 20s, Nicholls appeared in several films, including David Lynch's The Elephant Man (1980). Other feature film credits include Nic Roeg's Heart of Darkness, James Ivory's Maurice, and the 1995 feature Persuasion. But it was her role as Cordelia Flyte in the iconic 1981 Brideshead Revisited that would change her life; she married Brideshead director, Charles Sturridge in 1985.

Nicholls' other television credits include MASTERPIECE episodes of Foyle’s War, Inspector Lewis, and Prime Suspect 6. Her extensive theater work includes appearances alongside Sir Anthony Hopkins in David Hare's 1985 satire, Pravda.