Heath was born in Burma in 1920 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 Lancaster bombers in World War II, but spent almost the entire war as a prisoner of war at Stalag 383, where he started experimenting with abstract forms and shapes whilst in solitary confinement following his attempt to escape. The war years proved crucial in the development of Heath’s analytic, abstract approach to form, which he always privileged over realism and figuration. Asked by the Stalag newspaper, Camp, what spiritual lesson captivity had taught him, Heath answered, “to observe at first-hand how people of any background, education, temperament, intelligence and ability can respond to art and benefit from doing it and talking about it”. During this period he also 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. He was also influenced by D'Arcy Thompson. This period saw Heath becoming a significant figure in promoting abstract art by organising collective exhibitions at his London studio and by writing a short popular book, ‘Abstract Painting: Its Origin and Meaning’, 1953. This book begins with the statement: “There seems to be little understanding of the values of abstract painting and consequently no general appreciation of its qualities.” The exhibitions helped to inspire Lawrence Allowy’s book ‘Nine Abstract Artists’, 1954. Heath’s paintings of this time featured large, block-like slabs of colour, heavily brushed. He also made a few constructions. Later his paintings became freer and more dynamic.

Heath taught at Bath Academy of Art (1955–76) and the University of Reading (1980–85). He was artist in residence at the University of Sussex in 1969 and a senior fellow at the Glamorgan Institute of Higher Education, Wales (1977–80). He was a member of 56 Group Wales from 1978 to 1982.

He exhibited at the Musée Carcassonne in 1948, and at the Redfern Gallery, London, from 1953, together with other galleries in London. His work is in the collections of the Tate Gallery and the Hirshhorn Museum, Washington DC. He is well represented in collections all over the world, including the Tate, British Museum and the Brooklyn Museum in New York.