Benjamin studied at the RCM and after serving in the infantry and the air force in WWI, joined the staff of the RCM in 1926.
His early compositions were influenced by Gershwin, although such an influence is difficult to find upon hearing his work. An accomplished pianist, his ability on the instrument also played an important role in his work. A later and more productive influence was that of Latin American music. One of his most popular pieces and the one that gained him international recognition is the Jamaican Rumba (1938). The majority of his work is light and jovial in character. Although he did write some serious compositions, they were infrequently performed and his fame rests with his lighter work. He also composed for film, an example of which is the score for the 1947 movie An Ideal Husband.