However, he was then cast as an Australian soldier in A Town Like Alice (1956), which became the third most popular film at the British box office in 1956 and won Finch a BAFTA for Best Actor. He followed it with The Battle of the River Plate (1956), playing Captain Hans Langsdorff. This was also successful financially and British exhibitors voted Finch the seventh most popular British star at the box office for 1956.
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.
Finch co-wrote and directed an award-winning short film, The Day (1960) and announced plans to direct a feature but it did not eventuate. He won his third BAFTA for Best Actor for No Love for Johnnie (1961), although like Oscar Wilde, the film lost money. He was originally chosen to play Julius Caesar in Cleopatra (1963) and filmed scenes in London, but when the film was postponed he withdrew; the role was recast with Rex Harrison.