Professor Thompson graduated from St. Andrews University with a first class joint honours degree in Economics and Modern History in 1974. He pursued a Masters degree in Economic and Political Thought at the Queen's University Belfast before receiving his doctorate from the University of Cambridge in 1981. He spent a short time in the Economic Intelligence Department of the Bank of England before being appointed as a lecturer in Economic History at Swansea University in 1979.
He was awarded a personal chair in 1999, was Head of the Department of History from 2000 to 2005. He became Head of the School of Humanities in 2005and was appointed Pro-Vice-Chancellor in 2008.
Professor Thompson is a Fellow of the Royal Historical Society and is on the editorial board of Labor History.