Heath was born in Burma and attended Bryanston School in Dorset, southern England. In 1938, he studied art under Stanhope Forbes at Newlyn. In 1939 and 1945–47, he attended the Slade School of Art. He served in the RAF as a tail gunner in a Wellington bomber in World War II, but spent almost the entire war as a prisoner of war at Stalag 383. During this period he became friends with and taught fellow POW Terry Frost to paint.
In 1949 and 1951, he visited St Ives, Cornwall, where he met Ben Nicholson. In the early 1950s, he was also associated with Victor Pasmore and Anthony Hill. As such he became the main link between the emerging St Ives School and British Constructivism.