Born in Lincolnshire, Besley attended Aylesbury Grammar School, and then studied at Oxford University, where he gained a B.A. in Philosophy, Politics, and Economics (1st Class) from Keble College, Oxford and an M.Phil. and a D.Phil. in Economics having been elected an Examination Fellow of All Souls College, Oxford in 1984. At Oxford, he was one of the most successful students, evidenced by winning three George Webb Medley Prizes for his BA and M.Phil exam performance.