Gunn was an undergraduate and doctoral student at
Merton College, Oxford, matriculating in 1979. Prior to this he attended the
Whitgift School in
South Croydon. Gunn's doctoral thesis, a study of the life and career of
Charles Brandon, 1st Duke of Suffolk, was supervised by C. S. L. Davies and completed in 1986. Prior to being elected a Tutorial Fellow at his alma mater, Gunn held a research fellowship at
Newcastle University. Gunn's research interests lie in the political, social, cultural and military history of England and its European neighbours, spanning the mid-fifteenth to the late sixteenth century. Gunn was awarded the
Title of Distinction of Professor of Early Modern History by the University of Oxford in October 2015. Gunn delivered the 2015
James Ford Lectures in British History at the University of Oxford, taking as his subject 'The English people at war in the age of Henry VIII'. A book of the same title based on the lectures was published in 2018. Between 2018 and 2019 Gunn served as Acting
Warden of Merton College in the period between the retirement of
Martin J. Taylor and the arrival of his successor,
Irene Tracey. He had previously served as Sub-Warden from 2010 to 2012. In 2021 Gunn was appointed to the board of trustees of the
Royal Armouries by
Oliver Dowden, the
Secretary of State for Digital, Culture, Media and Sport, serving a four-year term. He was reappointed for a second four-year term by
Lisa Nandy in 2025. ==Media work==