Frank Adams's mother was Jean Mary Baines, a biologist, and his father was William Frank Adams, a civil engineer. He was the eldest of his parents two children, having one younger brother. The family was evacuated from London during World War II which somewhat disrupted his early education. As a consequence he attended school in a number of places but his education was mainly at Bedford School. By the time his schooling was completed World War II had ended but Britain still had national service and all young men were required to serve for two years. Adams served in the Royal Engineers during 1948 and 1949 before beginning his university education.