She began her career as a dancer in West Endmusic halls, making her film debut in How's Chances? (1934) in a small part, and had a larger role in another 1934 film, Get Your Man. She continued to act in "quota quickies" films for several years. Walsh first met David Lean, then a film editor, in 1936, during the filming of Secret Of Stamboul. They began a relationship and Walsh broke off her engagement to Pownell Pellew. Walsh and Lean married on 23 November 1940. She moved on to higher-prestige films with appearances in two Noël Coward-scripted films, In Which We Serve (1942) and This Happy Breed (1944), both directed by Lean. Walsh had campaigned for Lean to receive co-director credit on In Which We Serve.
Walsh contributed dialogue to the 1938 film of Pygmalion, and also devised the scenario for the closing sequence of Lean's film adaptation of Great Expectations (1946), for which she received a writing credit on the latter film. She devised the opening sequence of Lean's adaptation of Oliver Twist (1948), as well as performing the role of "Nancy". Walsh and Lean divorced in 1949, on grounds of infidelity based on Lean's relationship with actress Ann Todd. Walsh continued to work as a character actress in films through the 1950s, including films with Alfred Hitchcock and Ronald Neame. Her own favourite film role was that of the barmaid Miss D. Coker in Neame's 1958 film of The Horse's Mouth, with Alec Guinness.
Between films, she appeared regularly in plays and farces at the Strand and Aldwych theatres, directed by Basil Dean. She was a semi-regular on the 1979 Anglo-Polish TV series Sherlock Holmes and Dr. Watson, and remained active in films until her retirement in 1981. Her last role was in Night Crossing.