The eldest son of parents who were both members of the Salvation Army, Mileson and his four siblings were born in Pennywell, an estate in Sunderland, England. All the children were committed Christians who were given a good education, brought up in a poor household. Told he would never make the sports team after breaking his back in a quarry aged 11, Mileson took up running. He won the bronze medal in the 1967 English cross country junior championships – then immediately stopped: "It was the happiest day of my life. I hated every minute of running, but I had something to prove."
