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.
During this time, Finch continued to appear on stage in various productions while under contract to Olivier. Finch's closeness to the Olivier family led to an affair with Olivier's beautiful but increasingly unstable wife, Vivien Leigh, which began in 1948, and continued on and off for several years, ultimately falling apart due to her deteriorating mental condition.
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.