Rance was born in Southend-on-Sea, the youngest of five children of the Rev Frederick Ernest Rance, vicar of All Saints Church. Shortly after he was born the family moved to St Margaret's, Leytonstone, where Frederick Rance held a daily early morning service for the local milkmen at 5am. Rance's obituarist in "The Times" comments, "A respect for dairy workers was thus instilled in Rance from his earliest years." He was educated at Christ's Hospital from where he went on to the Royal Military Academy, Sandhurst in 1936. He was commissioned in the Northamptonshire Regiment in 1938. When the Second World War broke out he was seconded to the Buffs (Royal East Kent Regiment) , where he was adjutant of a wartime battalion, and taught a number of his men to read and write. He was promoted to major at the age of 24, and served at the Battle of Anzio in 1944. After the war he was employed in Vienna on intelligence duties. He retired from the Army in 1949 and worked for two years at Conservative Central Office in London.