|The Life and Death of Colonel Blimp (1943) [Edith Hunter/Barbara Wynne/Angela 'Johnny' Cannon]: Playing three different roles, two of her characters die off-screen of unspecified natural causes. "Barbara's" death is reported by a newspaper clipping in a montage showing the passage of time, and "Edith's" death is reported by Anton Walbrook when he explains his history to a British official. (Her third character, "Johnny," survives the movie.)
Edward, My Son (1949) [Evelyn Boult]: Dies (off-screen) of alcohol-related illness; her body is not shown, but we see her gravesite afterwards. (Thanks to Artur)
Julius Caesar (1953) [Portia]: Commits suicide (off-screen) by swallowing hot coals; we only see a scene of James Mason describing her death to John Gielgud after receiving the news.
Young Bess (1953) [Catherine Parr]: Dies of an unspecified illness. (Historically, Catherine Parr of complications a few days after childbirth, but the synopsis I've read indicates that a great many liberties were taken with the facts.)
The End of the Affair (1955) [Sarah Miles]: Dies (off-screen) of tuberculosis; we learn of her death when Peter Cushing and Frederick Leister come downstairs and inform Van Johnson and Nora Swinburne. (See also Julianne Moore in the 1999 version.)
Bonjour Tristesse (1958) [Anne Larson]: Commits suicide by driving her car over a cliff. (Thanks to El Kabong)