After graduating in Chemistry in 1980 from the University of Oxford, Graham worked in the Science Faculty of the Open University for three years. He joined the central administration at Cambridge in 1983 and held a number of posts, including Secretary of the School of the Humanities and Social Sciences.
In 1996 he became Deputy Secretary General of the Faculties and subsequently Academic Secretary of the University a post which he held until 30 September 2015. In this role, he was Secretary of the General Board and Head of the Academic Division with wide-ranging responsibilities for the University's teaching and research and for academic strategy.
He has been a Fellow of Wolfson since 1999 and served as the College’s Vice-President from October 2015 to December 2022. He is currently Chair of the Finance Committee and the Arts Committee, as well as Senior Treasurer of the Boat Club.
He is also a Trustee/Director and Deputy Chair of the Babraham Institute.
He has served as a Governor of Bromsgrove School, the Papworth NHS Foundation Trust and as a member (including terms as Chair and Secretary) of the University’s Board of Scrutiny.