Graham graduated in botany from Manchester University where he also completed a PhD in plant pathology.
He worked at Plant Breeding International (formerly Plant Breeding Institute) in Cambridge for 27 years on resistance to diseases of various crops and was Head of Plant Technology from 1995.
In 1999 he was appointed Director of Research and Development at HGCA (Home-Grown Cereals Authority) and he retired from that position in 2009.

Graham is a Special Professor at Nottingham University and has recently been appointed Chairman of Crop Evaluation Ltd, the company which manages the Recommended Lists for Cereals and Oilseeds.