Born in Leeds, Heron lived in Cornwall for several years as a child, and he eventually settled in Zennor, St. Ives, taking over Nicholson's studio in 1958. He studied at Slade School of Fine Art, 1937-39. During the Second World War, he was a conscientous objector and so worked on the land and also spent a short time at Leach Pottery in St. Ives.

He returned to painting in 1945 and had his first solo show at Redfern Gallery in 1947. He was also an increasingly important art critic, writing for New English Weekly, New Statesmen and Nation, and for Arts, which was based in New York. He also taught at the Central School of Arts and Crafts 1953-56.

In the mid-1950s Heron began to paint abstract works, and became one of Britain's strongest links with the New York Abstract Expressionists. His works using vibrant colour soon became unmistakeable, and from 1960 were shown in several solo exhibitions at Bertha Schaefer Gallery, New York and widely elsewhere abroad.

Retrospectives of his work have been held at the Whitechapel Gallery in 1972, the Barbican Art Gallery in 1985 and the Tate Gallery in 1998. His work is held in many major collections, including the Tate Gallery and the V&A.