Barron began his playing career at Wolverhampton Wanderers in 1961. After time in the reserves, he made his league debut on 30 November 1963 in a goalless draw with Everton. He managed 7 starts in the 1963–64 season, deputising for Fred Davies, but apart from a solitary appearance the following season, these proved his only games for the club.
He moved to Chelsea in 1965 but found opportunities just as limited. It was only when he joined lower league Oxford United the following year that he gained regular football.
Barron is currently a first-team coach at League OneNorthampton Town, and was appointed as joint caretaker manager on 20 December 2006, following the resignation of John Gorman. After the appointment of Stuart Gray as new manager in January 2007, Barron reverted to his role as a first team coach.