The son of James Julian Graydon and Rita Mary Graydon (née Alkan), Graydon was educated at Wycliffe College, in the town of Stonehouse in Gloucestershire, and became a flight cadet at the Royal Air Force College Cranwell in January 1957 before being commissioned into the Royal Air Force on 15 December 1959. His potential as a flying instructor was noticed early in his career and, after completing his Qualified Flying Instructor course at the Central Flying School, he was posted to No. 1 Flying Training School at RAF Linton-on-Ouse in Yorkshire in 1960. Promoted to flying officer on 15 December 1960, he attended No. 229 Operational conversion unit where he gained experience on the Hunters before being sent to No. 56 Squadron at RAF Wattisham, from where he flew Lightnings, in 1962.