Hunnicutt attended the University of California, Los Angeles on a scholarship to study English literature and theatre.

She played Charlotte Stant in the Jack Pulman television adaptation (1972) of Henry James's The Golden Bowl.

She played Ann Barrett in The Legend of Hell House (1973) and Tsarina Alexandra in the television miniseries Fall of Eagles (1974).

She appeared as Irene Adler, opposite Jeremy Brett, in the first episode of the TV series The Adventures of Sherlock Holmes ("A Scandal in Bohemia") in 1984.

Hunnicutt returned to the United States in 1989 to play the role of Vanessa Beaumont in Dallas, making semi-regular appearances until 1991.

In 2012, Hunnicutt was featured in an episode of the HGTV reality show Selling London, in which she presented the Primrose Hill estate where she and her second husband, journalist and editor Simon Jenkins, lived for three decades.