William Cooper was born in Crewe, and educated at Christ's College, Cambridge. After graduating in 1933 he was a teacher in Leicester, the setting for the 'first' novel Scenes from Provincial Life (1950), which would be the first of five featuring the character Joe Lunn. There followed, in order of writing, Scenes from Metropolitan Life, Scenes from Married Life, Scenes from Later Life and Scenes from Death and Life. However, Metropolitan Life, written in the mid-50s, remained unpublished until 1982 (after the death of C. P. Snow in 1980), for legal reasons. Scenes from Death and Life, his last published work, was turned down by Hoff's publisher Macmillan and was issued by a small independent company.

Hoff served in the Signals Branch of Royal Air Force in World War II, and later became a civil servant, associating closely with C. P. Snow, who appears in light disguise as Robert in the Scenes novels. Amongst his appointments he worked for the UK Atomic Energy Authority and the Crown Agents. After retiring he held an academic position.

Snow and Hoff evidently discussed the technique of novel writing extensively; and their books show clear parallels, if not in subject matter, where Hoff took the 'low road'. The theme of habit (and also illness) that Snow seems rather consciously to borrow from Proust is used with greater subtlety; while on the other hand the view of people is perhaps deliberately cruder.

In 1966 Scenes from Provincial Life and Scenes from Married Life were adapted for a seven-part ITV1 series, You Can't Win, starring Ian McShane.