Stone was born on 4 December 1919 in Epsom, Surrey, England. He was educated at Charterhouse School, an all-boys public school (i.e., an independent boarding school). He studied for a time at the Sorbonne in Paris in 1938. He then studied modern history at Christ Church, Oxford from 1938 to 1940. His university studies were interrupted by service during the Second World War as a lieutenant in the Royal Naval Volunteer Reserve. He returned to Oxford after demobilisation in 1945, and after a further year of study, graduated with a first-class Bachelor of Arts (BA) degree in 1946. As per tradition, his BA degree was promoted to a Master of Arts (MA Oxon) degree.