In 1934–35 he appeared in a number of productions for Doris Fitton at the Savoy Theatre, some with a young Sumner Locke Elliott. He also worked as a sideshow spruiker at the Sydney Royal Easter Show, in vaudeville with Joe Cody and as a foil to American comedian Bert le Blanc. At age 19 Finch toured Australia with George Sorlie's travelling troupe.
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.