Born in Sydney, Cornforth was the son and the second of four children of English-born, Oxford-educated schoolmaster and teacher John Warcup Cornforth and Hilda Eipper (1887–1969), a granddaughter of pioneering missionary and Presbyterian minister Christopher Eipper. Before her marriage, Eipper had been a maternity nurse.
Cornforth was raised in Sydney as well as Armidale, in the north of New South Wales, where he undertook primary school education.
At about 10 years old, Cornforth had noted signs of deafness, which led to a diagnosis of otosclerosis, a disease of the middle ear which causes progressive hearing loss. This left him completely deaf by the age of 20 but also fatefully influenced his career direction away from law, his original intended field of study, and towards chemistry. In an interview with Sir Harry Kroto for the Vega Science Trust, Cornforth explained: