Barron began his academic career in Cambridge University where he took a PhD in the Cavendish Laboratory.
In this role he led the Cambridge efforts to develop the Titan Supervisor (a multi-programming operating system) and CPL (Combined Programming Language).
The CPL project broke new ground in language design and application generality, and the resulting defining paper was written by the original development team.
Barron left Cambridge in 1967 to take up a chair of computer science at the University of Southampton where he remained until his retirement in 2000.
In 2009, on the 60th anniversary of the completion of the Cambridge EDSAC computer, he delivered a seminal lecture on what was involved in programming this pioneering machine in the 1950s.