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He was educated at Bishop Vesey's Grammar School and at the University of Birmingham (BSc, PhD). He began his career as a research fellow in chemistry at Yale, before becoming a lecturer in biological chemistry at the University of Aberdeen. He then served as Professor of Biological Sciences at the University of Warwick from 1969–82, and Eleanor Roosevelt fellow at the University of Colorado from 1975-76. He was appointed Vice-Chancellor of the University of East Anglia in 1987 and held the post until 1995. He was awarded a CBE in 1994 and is a deputy lieutenant of Norfolk. He lived in Cringleford. He was an Honorary Fellow of St Edmund's College, Cambridge.
Burke died on 15 March 2019.
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