She began film acting in 1936, with her more famous roles being Vera Charles in "Auntie Mame" (1958), Mercy Croft in "The Killing of Sister George" (1968), and Lady Claire Gurney in "The Ruling Class" (1972). Her television debut came in January 1938, when she appeared in a BBC Television production of "The Billiard Room Mystery". Throughout her career, she was a regular performer on BBC Radio and appeared in numerous radio dramas, including "Dinner at Eight", "The Second Mrs. Tanqueray", "The Caspary Affair", "The Tragedy of Othello", "Oedipus The King", "Hamlet", "The Infernal Machine", "Two Mothers", "Captain Brassbound's Conversion" and "The Eyes of Youth" amongst many others. In 1961, Browne was the featured castaway on "Desert Island Discs", hosted by Roy Plomley. Television plays for the BBC included "Charley's Aunt" in 1969, "Lady Windermere's Fan" in 1972, "Mrs. Warren's Profession" also in 1972 and "The Importance of Being Earnest" in 1974.