Mansfield was born in Lambeth, London on 9 October 1933, to Sidney George (b. 1904, d. 1966) and Lillian Rose Mansfield (b. 1905, d. 1984; née Turner). Mansfield was the youngest of three sons, Conrad (b. 1925) and Sidney (b. 1927).
Mansfield grew up in Camberwell. During World War II he was evacuated from London, initially to Sevenoaks and then twice to Torquay, Devon, where he was able to stay with the same family on both occasions. On returning to London after the war he was told by a school master to take the 11+ exam. Having never heard of the exam before, and having no time to prepare, Mansfield failed to gain a place at the local Grammar school. His mark was, however, high enough for him to go to a Central School in Peckham. At the age of 15 he was told by a careers teacher that science wasnt for him. He left school shortly afterwards to work as a printers assistant.
At the age of 18, having developed an interest in rocketry, Mansfield took up a job with the Rocket Propulsion Department of the Ministry of Supply in Westcott, Buckinghamshire. Eighteen months later he was called up for National Service.