On stage, she has appeared in many productions as well those with the Bristol Old Vic, the Royal Shakespeare Company and the Royal National Theatre. Her early film roles have included Catherine Parr in Henry VIII and His Six Wives (1972), Bequest to the Nation (1973), Oh Heavenly Dog (1980), and most famously in Alfred Hitchcock's penultimate film Frenzy (1972), as a woman raped and strangled by a serial killer.

In 1983 Leigh-Hunt appeared as the Queen of Bavaria in the mini-series Wagner sharing her scenes with Ralph Richardson, Laurence Olivier and John Gielgud as court ministers. Richard Burton played the Composer Richard Wagner and her husband Richard Pasco appeared also.

She also played Jean Lawrence in the controversial BBC drama Tumbledown (1988), and Lady Catherine de Bourgh in Pride and Prejudice (1995), and provided the voices of the farmer's wife in The Plague Dogs (1982), and Captain Mildred and Mary the Hover Fairy in the 1987 Children's BBC series Charlie Chalk. In 1999, Leigh starred as Lady Cumnor in BBC's four-part series adaptation of the novel Wives and Daughters (1999). More recently she has appeared in such films as Paper Mask (1990), Keep the Aspidistra Flying (1997), Billy Elliot (2000), The Martins (2001) and Vanity Fair (2004), and has had much work on television, mainly in guest character parts.