He was a student at the University of Leeds, where he read English and Modern Languages, graduating in 1932. He had a brief teaching career, in Dagenham.

Coming to London in 1934, he rapidly made initial contacts in the literary world. A short study Middleton Murry: A Study in Excellent Normality (1934) brought him for a time into John Middleton Murry's Adelphi commune at "The Oaks", where in 1935 he worked as a cook. In 1935, also, he met Dylan Thomas, sent to meet him by Sir Richard Rees of the Adelphi magazine. In short order he became a Catholic convert, and married Margaret Edwards in 1937. In the mid-1930s he was influenced by Eric Gill.

He was a friend of George Orwell, encountered also in 1935 through Thomas and Rees, and later wrote about him in his memoir Four Absentees. Heppenstall, Orwell and the Irish poet Michael Sayers shared a flat, in Lawford Road, Camden. Heppenstall once came home drunk and noisy, and when Orwell emerged from his bedroom and asked him to pipe down, Heppenstall took a swing at him. Orwell then beat him up with a shooting-stick, and the following morning told him to move out. Friendship was restored, but after Orwell's death, Heppenstall wrote an account of the incident called The Shooting-Stick.

During World War II, he was in the British Army, but with a Pay Corps posting at Reading, close enough to remain in touch with literary Fitzrovia. He was also posted to Northern Ireland.

Heppenstall's first novel The Blaze of Noon (1939), was neglected at the time. Much later, in 1967, it received an Arts Council award. He was Francophile in literary terms, and his non-fiction writing reflects his tastes.

Critical attention has linked him to the French nouveau roman, in fact as an anticipator, or as a writer of the "anti-novel". Several critics (including, according to his diaries, Hélène Cixous) have named Heppenstall in this connection. He is sometimes therefore grouped with Alain Robbe-Grillet, or associated with other British experimentalists: Anthony Burgess, B. S. Johnson, Ann Quin, Alan Burns, Stefan Themerson and Eva Figes. The Connecting Door (1962) is singled out as influenced by the nouveau roman.

He was certainly influenced by Raymond Roussel, whose Impressions of Africa he translated. Later novels include The Shearers, Two Moons and The Pier. He also wrote a short study of the French Catholic writer Léon Bloy (Cambridge: Bowes & Bowes, 1953).

From 1945 to 1965 he worked for the British Broadcasting Corporation on radio, as a feature writer and producer; and then for two further years as a drama producer. One of his early adaptations was of Orwell's Animal Farm, in 1947.

In his journals Heppenstall mentions problems he had with Evelyn Waugh regarding a radio broadcast in the 1940s. Waugh apparently felt that Heppenstall purposely insulted him, when he was sent to take him to the broadcast.