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 did radio acting work with Hugh Denison's BSA Players (for Broadcasting Service Association, later to become Macquarie Players). He came to the attention of Australian Broadcasting Commission radio drama producer Lawrence H. Cecil, who was to act as his coach and mentor throughout 1939 and 1940. He was "Chris" in the Children's Session and the first Muddle-Headed Wombat.
Finch returned to Australia to make The Shiralee (1957), one of his favourite parts, and the tenth most popular movie at the British box office that year. He followed it with another Australian story, the bushranger tale Robbery Under Arms (1957), which did less well. However exhibitors still voted Finch the third most popular British star of 1957, and the fifth most popular overall, regardless of nationality.
The number of Race to Dubai points available in the last three events of the season was increased, and the field size reduced. The aim was to make more players still have a chance of winning the Race to Dubai entering the final events. In addition, although the prize money was not increased, the bonus pool of US$5m would now be split among the top five players rather than the top ten. The money saved from restricting field sizes was used solely to increase the first prizes, which means that the tournaments would not have the standard prize fund distribution, and the DP World Tour Championship, Dubai would have the largest tournament first prize in golf of US$3m.