George Finch was born in New South Wales, Australia, but was educated in Paris and Zürich. He was a research chemist when he moved to Britain in 1912 and later served during the First World War with the Royal Army Ordnance Depot and the Royal Field Artillery. In 1915, at Portsmouth, Hampshire, George married Alicia Fisher, the daughter of a Kent barrister. However, George Finch was not Peter Finch's biological father. He learned only in his mid-40s that his biological father was Wentworth Edward Dallas "Jock" Campbell, an Indian Army officer, whose adultery with Finch's mother was the cause of George and Alicia's divorce, when Peter was two years old. Alicia Finch married Jock Campbell in 1922.
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.