Exeter-born Graham Moxham had been with both Preston and Bournemouth as a youngster before he joined Exeter City from Bideford in 1975. Making his Football League debut at the age of twenty-eight, he played half-a-dozen times before moving on to Barnstaple Town.

Although born in Exeter, Graham started his career as an apprentice at Preston North End and later became a full professional  with Bournemouth in July 1966. Not making the first-team at either club, Graham returned to Devon and played non-league football until joining Exeter City from Bideford in July 1975.

At the age of 28, Graham finally made his Football League debut when appearing as a substitute in a 2-1 home defeat against Cambridge United in September 1975. Subsequently starting four games, he made his final bow for the club - as a substitute - against Doncaster Rovers at the end of November. 

Leaving St James’ Park, Graham continued his non-league career with Barnstaple Town.