Robson was born in Haltwhistle in Northumberland and attended the Queen Elizabeth Grammar School in Hexham. After National Service in the RAF he entered Trinity on a state scholarship in 1950 to study History, taking first class honours in 1953. He then stayed on to complete a PhD under G S R Kitson Clark. The academic year 1956-57 was spent teaching at Glasgow University before returning to Trinity to take up the Fellowship which he held until his death.
For many years, Robson was involved in the business of being a tutor. He was Tutor for Advanced Students from 1960-64, Tutor for side C from 1964-74 and Tutor for Admissions 1979-88. He was involved with a number of college committees, notably the gardens committee and the buildings committee where his extensive knowledge of college history was of great use.
Robson published little. His first volume, The English Attorney in the Eighteenth Century (1959) has been seen as groundbreaking in the study of the rise of the professions. He contributed to and edited Ideas and institutions of Victorian Britain, the festschrift for George Kitson Clark and regularly wrote articles on aspects of college history for the Trinity Review. He revised Trevelyan’s Trinity College: An historical sketch and the pamphlet Trinity College: A short history and guide. For many years he worked on preparing an edition of Macaulay’s journal, although he never completed the work. Other projected works included a biography of Whewell and a history of the college.