- Honorary Fellow, All Souls College (from 2015)
- Distinguished Fellow, All Souls College (from 2001 to 2015)
- Pro-Vice-Chancellor, University of Oxford (from 1988 to 2000)
- President of Corpus Christi College, Oxford (from 1986 to 2000)
- Professor of Modern History (1986); Reader (1978-85), Fellow (and Tutor from 1957 to 1985) of St John’s College, Oxford (from 1957 to 1986)
- Examination Fellow, All Souls College (from 1955 to 1957)
- Senior Scholar, St Antony’s College, Oxford (1955)
- Brackenbury Scholar, Balliol College, Oxford (from 1952 to 1955)
- Social and cultural history of early modern England
- In Pursuit of Civility: Manners and Civilization in Early Modern England (London: Yale University Press, 2018)
- The Wolfson History Prize 1972-2012: An Informal History (London: Wolfson Foundation, 2012).
- The Ends of Life: Roads to Fulfilment in Early Modern England (Oxford: Oxford University Press, 2009).
- Changing Conceptions of National Biography: The Oxford DNB in Historical Perspective (Cambridge: Cambridge University Press, 2005).
- (ed.), The Oxford Book of Work (Oxford: Oxford University Press, 1999).
- Man and the Natural World: Changing Attitudes in England, 1500-1800 (London: Allen Lane, 1983).
- (ed. with Donald Pennington), Puritans and Revolutionaries (Oxford: Clarendon Press, 1978).
- Religion and the Decline of Magic (London: Weidenfeld and Nicolson, 1971).
- Honorary Vice-President, Royal Historical Society (from 2001)
- Chairman, Advisory Council, Warburg Institute (from 2000 to 2008)
- Trustee, British Museum (from 1999 to 2008)
- Chairman, British Library Advisory Committee for Arts, Humanities and Social Sciences (from 1997 to 2002)
- President, British Academy (from 1993 to 1997)
- Member, Academia Europaea (from 1993)
- Trustee, National Gallery (from 1991 to 1998)
- Member, Reviewing Committee on Export of Works of Art (from 1989 to 1992)
- Member, ESRC (from 1985 to 1990)
- Delegate (1980-2000) and Chairman of Finance Committee (1988-2000), Oxford University Press
- Foreign Honorary Member, American Academy of Arts and Sciences
- Honorary Member, Japan Academy
- Fellow, Learned Society of Wales
- Honorary DLitt: Columbia, Kent, Wales, Hull, Leicester, London, Sussex, Warwick
- Honorary LittD: Sheffield, Cambridge
- Honorary LLD: Williams, Oglethorpe
- Honorary PhD: Uppsala
- Honorary Fellow of Balliol, Corpus Christi, and St John’s Colleges, Oxford; University of Cardiff; and Warburg Institute, University of London