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Born in Manchester, his father was a Church of England clergyman and a scholar, and his mother had been a school mistress. Hopkinson attended prep school on the Lancashire coast and then St Edward's School, Oxford. From there he went to Pembroke College, reading Classical Moderations (Class II, 1925) and Greats (Class III, 1927). His philosophy tutor for Greats was R. G. Collingwood.