In 1969 local boy Graham captained Ladysmith school to several trophies and played in every game for the Exeter & District side that swept the board of trophies culminating in a quarter final exit in the English schools FA Cup away to Brighton at the Goldstone ground where the team were given a mayoral civic reception .
He also played many games for Devon schools. Upon leaving school Graham was signed by Theo Foley in August 1970, where he was coached by Theo and Maurice Setters he was also team mates with Allen Clarke & Dick plumb (all with city connections future or past).

Graham made his debut for Charlton reserves at Craven Cottage and went on to play in 42 reserve games and many youth games . He also played in several 1st team friendlies against youth players at the time Graham Souness, Liam Brady, Glen Hoddle and Ray Wilkins before injury ended his time at the valley.

Returning to Exeter John Newman signed Graham on amateur forms with a view to signing him professionally, training with the first team and following several promising displays with the reserves acknowledged in the local press and match day programmes, (see below),Graham was hospitalised where a hernia operation was needed, so putting and end to his season.

The following was such an article in a programme written by Richard Knight 

"Although the reserves have not yet settled down upon their re introduction to the Western League circuit, one of the amateurs has already caught the eye. He is Graham Browne and has had a series of good games at left-back. Graham has just returned to Exeter after a spell as an apprentice with Charlton Athletic"

The following 1974/75 season saw Graham back training with the Exeter only to suffer a terrible knee injury in pre season training, forcing him out of the game for a year. Whereupon, future City coach Chris Davey signed him for Dawlish Town with a view to fast tracking him for a much needed knee operation which subsequently proved unsuccessful and unfortunately despite many attempts Graham was forced to retire from the game at 23 years old.

Graham was a substitute for Exeter City reserves in the Western League at Weston-Super-Mare, on the 27th of January 1974. He was still playing the following season for the reserves, He played against Bodmin, in a South Western League game for Exeter City on the 20/1/1975.