Dunham, born in Dorset, moved to Durham with his family early in life and attended the Johnston School. At Durham University he studied geology under Arthur Holmes (q.v.) and was also a talented organ scholar.

Dunham's classic work was Geology of the North Pennine Orefield and he became Professor of Geology at Durham 1950-71. He supervised the Rookhope borehole and became Director of the British Geological Survey in 1967. He was knighted in 1972.