Born in St. George's, Grenada, Batson moved with his family to England when he was nine. Until then he had never even seen a game of football and a teacher at this school, on watching his early efforts and reflecting on his birthplace opined, "Well, perhaps cricket is your game." However, he was signed as a schoolboy by Arsenal, and was the first black player to play for the Gunners' first team. In all, he made 10 appearances for Arsenal before moving to Cambridge United in 1974. He spent four years at Cambridge, captaining the side to the Fourth Division Championship under manager Ron Atkinson in 1976-77. When Atkinson moved to West Bromwich Albion in 1978, he attracted Batson to follow him and to team up with fellow black players Cyrille Regis and Laurie Cunningham. Although not by any means the first black footballers to play professionally in England, the Three Degrees (a reference to The Three Degrees contemporary vocal trio of the same name) were an integral part of their acceptance in the English leagues.
A cultured defender, Batson's career was cut short by a serious playing injury in 1982, following which he developed into an able and active administrator at the Professional Footballers' Association. He was capped three times for the England B team.