Walker was born in Halifax, Yorkshire, the son of Thomas Ernest Walker, a stonemason, and Elsie Lawton, an amateur musician. He was brought up with his two younger sisters (Judith and Gen) in a rural environment and went to Rastrick Grammar School. At school, he was a keen sportsman and specialized in physical sciences and mathematics the last three years. He received a Bachelor of Arts degree in Chemistry from St Catherine's College, Oxford. Walker began his study of peptide antibiotics with Edward Abraham at Oxford in 1965 and received his Doctor of Philosophy degree in 1969. During this period, he became interested in developments in molecular biology.