Finch was born into a music hall and travelling theatrical family in London and was taken to the United States as a young child.

There she worked with Fatty Arbuckle, Mack Sennett (with whom she was reportedly involved romantically for a short time), Charlie Chaplin, and other leading performers and producers of the silent era.

Those shorts, known as "Bunnygraphs", "Bunnyfinches", and "Bunnyfinchgraphs", established Finch and Bunny as the first popular comedy team in films.

One of her best-known roles in the later silent years was Aunt Susan in Paul Leni's The Cat and the Canary (1927).

The Scarlet Letter (1934) gave her one of her more substantial roles in sound films, and she had a cameo in one of Laurel and Hardy's best-known features, Way Out West (1937).