In 1967, she accepted the Oscar for best actor in a leading role on behalf of Paul Scofield (her co-star in A Man for All Seasons (1966)), who wasn't present at the awards ceremony.
She & husband Ronald Gow had one daughter and one son.
She played Eliza Doolittle in Pygmalion (1938) opposite Leslie Howard as Professor Henry Higgins. Rex Harrison, who also appeared in Major Barbara (1941) with Hiller, played Professor Henry Higgins in the Lerner and Loewe musical My Fair Lady on Broadway, followed by the West End London production (both opposite Julie Andrews as Eliza Doolittle) and in the My Fair Lady (1964) opposite Audrey Hepburn as Eliza Doolittle. He continued to appear in the role on and off in smaller productions for decades.
She was Sidney Lumet 's second choice to play Princess Dragonmiroff in Murder on the Orient Express (1974). Lumet's first choice was vetoed by the producers. 'Ingrid Bergman' was then offered the role and declined, instead choosing the role of Greta Ohlsson, and then the role was offered to Hiller.
She was awarded an honorary LLD by Manchester University in 1984.
She was awarded an OBE (Officer of the Order of the British Empire) in 1971 for her services to drama.
She was awarded the Dame Commander of the Order of the British Empire in 1975 for her services to drama.
She was buried next to her husband in the churchyard at St Mary's, Radnage, Buckinghamshire. The same church was used in the film A Month in the Country (1987).
She was nominated for Broadway's 1958 Tony Award as Actress in a Leading Role in a Drama for Eugene O'Neill's play, "A Moon for the Misbegotten.".
She was personally chosen by George Bernard Shaw to play the lead roles in 1930s productions of his plays Saint Joan and Pygmalion. She was reputedly his favorite actress of the time.