Hodgkin was born in London, and studied at Camberwell Art School and Corsham, near Bath. Related to the painter and art critic Roger Fry, who introduced post-impressionist painting to England, Hodgkin's work has affinities with a type of sensual, colourist painting that has not always been appreciated in the UK. In 1964 he made his first visit to India, and the influence of Indian miniature painting on his work has been profound, notably in his preference for flat colours and decorative borders. In the 1970s he began to amass a significant collection of Indian art.

Hodgkin had his first one-person show in 1962, and his reputation grew steadily, but it was while he was in his 40s that his work took off, as one critic wrote, "into the exhilarating freedom, boiling colour, and charged emotion that we think of as typically Hodgkin". Some observers associate this new freedom with his recovery in the 1970s from a near-fatal medical condition. Others maintain it has something to do with Hodgkin's acceptance and public announcement of his homosexuality at about the same time. However, the painter has denied this.