Tunnard was born at Sandyford, Bedfordshire in May 1900, and was schooled at Horton School and Charterhouse, where he won the Struan Robertson prize for drawing 2 years running.. Between 1919-1923 he studied at the Royal College of Arts, then worked as textile designer from 1923-1927. He worked as a part-time teacher of design at the Central School of Arts and Crafts from 1929, before exploring Cornwall and eventually making it his home.

A full chronology of his life is contained in the 1977 catalogue of the Arts Council exhibition, 'John Tunnard 1900-1971' - a major retrospective touring show which began at the RA, and progressed to Kettle's Yard, Kettering Gallery, Manchester City Art Gallery, Laing Art Gallery, Newcastle, finishing at the Newlyn Art Gallery in Penzance. The biography by Alan Peat and Brian Whitton (1997) is an elegant and thorough tribute to this important artist, including a catalogue raisonne and exhibition list.

The artist married a fellow student at the RCA in 1926, Mary May ROBERTSON ARCA, and painted landscapes and coastal scenes during the 1930s, coming to Cornwall on a 5-month camping expedition to paint on the Lizard, and continuing thereafter to paint in Cornwall whenever he could. After his first solo show at the Redfern Gallery in 1933, his sub-title being 'Paintings from Cornwall', he purchased a caravan and moved to Cadgwith on the Lizard, where he rented part of a fisherman's loft and began a hand-blocked silk industry with his wife.

In 1934 he joined the London Group and began to paint abstract works influenced by Klee, Miro and the British surrealist movement. During the 1930s his work often featured architectural, sculptural and biomorphic forms, combined with elements of constructivism. In 1939 he was given a show at the influential though shortlived Guggenheim Jeune Gallery in London, which was a pivotal moment in his career. Peggy Guggenheim bought one of his paintings, which led to the Museum of Modern Art (MOMA) in New York purchasing his 'Fugue' in 1944.

During World War II Tunnard worked as a coastguard while he and his wife kept their hand-blocked silk business going. He continued to exhibit not only in England but also in British Council exhibitions in Australia and South America, and had a solo show in New York in 1944.

During 1946 Tunnard had a brief spell teaching at the Wellington School in Somerset, before selling his cottage at Cadgwith and moving to Zennor in 1947. The following year he began teaching design at the Penzance School of Art, which he continued to do until 1965. In 1953 he moved to Lamorna, where he and Mary (known as Bob) created a beautiful and unusual home and spectacular garden at the head of the Valley, where Laura KNIGHT and her husband Harold KNIGHT once lived.

Some of his best work was carried out between 1958 and 1962. From 1960 he began to be hung regularly at the Royal Academy, and was made an ARA in 1967. Much of his work responded to world events such as the 1962 detonation of an atom bomb on the Johnston Atoll in the Pacific (for example, 'Aftermath'). His interest in the moon and space exploration found expression in 'In Many Moons' (1966-7) and 'Messenger' (1969).

At the death of his wife in 1970, he moved into a flat in Penzance, where he died the following year. The two artists are buried in Zennor churchyard.