He was educated at the Central Foundation Boys' School[1] in Cowper Street and went on to study medicine at University College Hospital, London.
[2] Having worked for a time as a general practitioner in the East End of London, he served as a medical officer in the Royal Air Force during World War II.
Having gained the Diploma in Psychological Medicine in 1945, Hamilton began his training as a psychiatrist at the Maudsley Hospital, London where, reputedly, he had difficulties with the rigid establishment.
He returned to University College Hospital as a part-time lecturer from 1945-1947 where he worked under the influence of Sir Cyril Burt who recognized Hamilton's mathematical talent and advised him to train in medical statistics.
[6] After working for two years as a visiting scientist at the National Institute of Mental Health, Bethesda, Maryland, USA, he became a member of the external staff of the Medical Research Council and in 1963 succeeded Ronald Hargreaves as the Nuffield Professor of Psychiatry at the University of Leeds, a post he held until his retirement in 1977.