Dexter was inspired to take A levels at night school and went on study physiology and zoology at the University of Salford. After graduating, he continued in academia and received a Doctor of Philosophy from the University of Manchester in 1974 for research into Leukemia. Dexter also received a Doctor of Science degree from the University of Salford in 1982.
Dexter was director of the Wellcome Trust, from 1998 to 2003. Dexter was visiting fellow at the Memorial Sloan–Kettering Cancer Center and a professor of haematology at the University of Manchester from 1985 to 1998. He was director of the Paterson Institute for Cancer Research and the Wellcome Trust.
He has authored over author of 360 articles in scientific journals like Nature and is an editor of four books
Royal Society.
