Professor Gough attended the Dragon School in Oxford before gaining a scholarship to Stonyhurst College where he concentrated on studying the Classics. In 1936 he gained a Classical Exhibition to Peterhouse College, Cambridge where he went on to become a Scholar and Prizeman. In 1939 he gained a First Class Honours Degree in the Classical Tripos with Archaeology as his specialism. With the outbreak of World War II in 1939 Gough joined the Royal Artillery as a Gunner, seeing service in the Middle East and throughout the whole of the Italian Campaign including during the battles of Cassino and on the Sangro. He was discharged from the Army in Germany in the Spring of 1946 with the rank of Major. In 1946 he married Dorothy Mary "née" Ormsby; together they took part in various excavations.