He was born in Inverness and educated at Edinburgh Academy and later at the English public school, Sedbergh, before proceeding to Christ Church in the University of Oxford in 1960 to read modern history. He graduated in 1963 and then moved to work as a teacher in East Africa, where he met his wife Sue Ann Curry (born 1941). They moved to Oxford in 1966, where they married, and Matthew began first an uncompleted diploma in politics and economics, and then a doctorate on the imperial wing of the Liberal Party in the 1890s and 1900s, completed in 1970.
In 1970 he was appointed lecturer in Gladstone studies at Christ Church, a post tied to the assistant editorship of the Gladstone Diaries, then being prepared for publication by M. R. D. Foot. In 1972 Matthew succeeded Foot as sole editor, and completed the project. In 1978 he was elected fellow and tutor in modern history at St Hugh's College, Oxford.
When Oxford University Press proposed a revision of the Dictionary of National Biography in the early 1990s Matthew's work on the Gladstone Diaries recommended him for the position. He began work in 1992 and devised the editorial structure and guidelines for the dictionary, as well as writing or revising several hundred articles for the work. He died from a heart attack in Oxford on 29 October 1999, but the dictionary was published in 2004 along the plan which Matthew had set out.
- McKibbin, R. I. (2004). "Matthew, (Henry) Colin Gray". In Matthew, H. C. G. and Harrison, Brian (eds.). Oxford Dictionary of National Biography. Oxford: Oxford University Press.
- Oxford Dictionary of National Biography (includes photo)