Educated at Alderman Newton's Grammar School, University College, Leicester and Christ's College, Cambridge, his 1936 doctorate on the social structure of the House of Commons of England under William III was supervised by G. M. Trevelyan. In 1939 he was elected to the Ehrman Fellowship, which was a research fellowship at King's College, Cambridge. After wartime service with the Foreign Office, he became a Fellow and Tutor of Christ's College and University Lecturer in History. In 1957 he was awarded a Doctor of Letters for his work on eighteenth-century history, and in 1962 he was appointed Reader in Modern History at Cambridge University.
Plumb was visiting professor at Columbia University in 1960. He was the European Advisory Editor for Horizon, and the advistory editor for history for Penguin Books. He was Master of Christ's College from 1978 to 1982. He became Professor of Modern English History in the University in 1966. He was elected a Fellow of the British Academy in 1968 and knighted in 1982.
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