Moore was the only child of policeman, George Moore, and housewife, Lilian "Lily". He attended Battersea Grammar School, but was evacuated to Holsworthy, Devon, during the Second World War. He was then educated at Dr Challoner's Grammar School in Amersham, Buckinghamshire. He then attended the College of the Venerable Bede at the University of Durham, but never graduated. Moore served in the Royal Army Service Corps, commanding a small depot in West Germany.