Finch's film roles increased in size and prestige through the early 1950s. For Walt Disney he played the Sheriff of Nottingham in The Story of Robin Hood and His Merrie Men (1952). He was given two good roles in films from Alexander Korda: as Richard D'Oyly Carte in The Story of Gilbert and Sullivan (1953), and as a priest in The Heart of the Matter (1953), from the Graham Greene novel.
Finch was nominated for an Oscar for Network and went on to posthumously win the award, which was accepted by his widow, Eletha Finch. Although James Dean, Spencer Tracy and Massimo Troisi were also posthumously nominated for a Best Actor Oscar, Finch was the first actor to have won the award posthumously, as well as the first Australian actor to win a Best Actor award. He was the only posthumous winner of an Oscar in an acting category until fellow Australian Heath Ledger won the Academy Award for Best Supporting Actor in 2009; there were many earlier posthumous Oscar winners in non-acting categories. Finch also won five Best Actor awards from the British Academy of Film and Television Arts (BAFTA), including one for Network.
He had a small role as an Australian prisoner of war in The Wooden Horse (1950), the third most popular film at the British box office in 1950. His performance as a Pole in Daphne Laureola led to his casting as a Polish soldier in The Miniver Story, the sequel to the wartime morale boosting film Mrs. Miniver; unlike its predecessor, it was poorly received critically.