After training at the prestigious Royal Academy of Dramatic Art, Stevenson became a company member of the Royal Shakespeare Company where she rose quickly from small roles to leads. Critics often compared Stevenson with the late Dame Peggy Ashcroft, notably for her direct ability to communicate with an audience and her facility with such roles as Isabella in "Measure for Measure" and Rosalind in "As You Like It." She was stunning as the virtuous Madame de Tourvel in Christopher Hampton's version of "Les Liaisons Dangereuse" (opposite Alan Rickman as Valmont), but did not to travel to Broadway with the company. Stevenson went on to join the National Theatre where she further solidified her standing as one of Britain's best stage actresses, tackling roles from "Yerma" to "Hedda Gabler." She more than held her own opposite John Malkovich in the West End production of Lanford Wilson's "Burn This" (1990) and garnered some of her best notices in her award-winning portrayal of a victim of political torture who turns the tables on her tormentor in "Death and the Maiden" (1991). Once again, the actress was passed over for Broadway (Actors Equity would not grant her a work permit and the role eventually went to Glenn Close) and when Roman Polanski directed the 1994 film version, he cast Sigourney Weaver. She finally made her American stage debut in the L.A. production of "Scenes From an Execution" in 1993. Stevenson had starred in the British TV series "Catherine Cookson's 'The Mallens'" for Granada TV in 1980 and won attention for her supporting work in "Life Story/Double Helix/The Race for the Double Helix" (BBC/A&E, 1987). Discerning American audiences also saw her fine portrayals of Nora in "A Doll's House" and in the title role of "The Politician's Wife" on PBS in 1992 and 1996 respectively.The actress entered films as one of a trio of woman who share both the same name and a murderous streak in Peter Greenaway's fascinating "Drowning By Numbers" (1987; released in the USA in 1991). Screenwriter David Hare provided Stevenson with a fine role as another grief-stricken woman in "The Secret Rapture" (1993), directed by Howard Davies. She also scored as the manipulative Mrs. Elton in Douglas McGrath's winning adaptation of Jane Austen's "Emma" (1996).