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Baker was born in Sheffield, the son of Kenneth Lee Vincent Baker, and Marjorie Baker (née Bagshaw). He was educated at King Edward VI Grammar School, Chelmsford, and University College London (LLB, PhD). He was called to the Bar at the Inner Temple in 1966 and was elected an Honorary Bencher in 1988.
His first academic post was as an Assistant Lecturer in Law at University College London, in 1965. In 1967 he was promoted to Lecturer, and in 1971 moved to the University of Cambridge. There he was Librarian of the Squire Law Library until 1973, and became a Fellow of St Catharine's College. His rooms were above the Sherlock Library until his retirement.
In 1973 Baker became a lecturer in Law at University of Cambridge. He was appointed Reader in English Legal History at the University of Cambridge in 1983. In 1988 he was appointed Professor of English Legal History. From 1998 until 2011 he was Downing Professor of the Laws of England.
He was President of St Catharine's College, Cambridge until 2007 when he was succeeded by Professor Sir Christopher Alan Bayly. He was also Literary Director of the Selden Society until 2011 (jointly with David Yale 1981-91, sole 1991-2011) when he was succeeded by Dr Neil Jones.
Appointments have included Visiting Professor, New York University School of Law since 1988, Visiting Fellow, All Souls College, Oxford in 1995, Honorary Fellow, Society for Advanced Legal Studies 1998, Corresponding Fellow American Society for Legal History 1992, and Foreign Honorary Member, American Academy of Arts and Sciences 2001. He was elected a Fellow of the British Academy (1984) and a Fellow of the Royal Historical Society (1980).
Baker was appointed a Fellow of University College London in 1991, awarded an Honorary LLD of the University of Chicago in 1991, and received the Yorke Prize (University of Cambridge) 1975, and the Ames Prize (Harvard Law School) in 1985. He was knighted in 2003, the only man ever knighted for services to legal history. In 2004, he was awarded the Irish Legal History Society's Gold Medal.
His first marriage in 1968 was to Veronica Margaret Lloyd, with whom he had two daughters. They were divorced in 1997, and in 2002 he married Fiona Rosalind Holdsworth (née Cantlay), who died in 2005. He remarried in 2010 to Elisabeth van Houts.
Interviews with Sir John Baker on ReConstitution, the website of The Constitution Society.