George gained custody of Peter, who was taken from his biological mother and brought up by his adoptive paternal grandmother, Laura Finch (formerly Black) in Vaucresson, France. In 1925 Laura took Peter with her to Adyar, a theosophical community near Madras, India, for a number of months, and the young boy lived for a time in a Buddhist monastery. Undoubtedly, as a result of his childhood contact with Buddhism, Finch always claimed to be a Buddhist. He is reported to have said: "I think a man dying on a cross is a ghastly symbol for a religion. And I think a man sitting under a bo tree and becoming enlightened is a beautiful one."
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.
Under the Big Top – touring show with George Sorlie, various Queensland towns, 1936, playing Herbert Hughes in Laughter of Fools by H.F. Maltby, Smithers in Married by Proxy by Avery Hopwood, Peter in Fair and Warmer by Avery Hopwood, Hunter in Ten Minute Alibi by William Armstrong – all directed by William McGowan with Murray Matheson, Rosalind Kennerdale, Leslie Crane, Eva Moss, Norman French, Julia Adair and George Douglas.