Having made 109 appearances for them, with loan deals at Bury and Wigan Athletic along the way, he was released on a free transfer to Stockport County for the beginning of the 1998–99 season, and quickly arrived at Burnley in January 1999, signed by the colourful manager Stan Ternent, following a falling-out with then Stockport manager, Gary Megson.

Once described by Ternent as a Premiership-standard player, his inability to hold down a regular position either as a left-winger, left-sided or central defender, or striker, saw him never play there.

His unpopularity with some supporters was balanced with him becoming something of a cult figure, earning him regular chants of "Graham di Branchio," (in reference to the football chant given to Italian footballer Paolo Di Canio), in an effort to boost his confidence and let his more prominent abilities such as pace and height come to the fore.

[3] The 2005–06 season held even more promise for the player after his hard work and commitment paid off after he was offered a new one-year extension to his current deal.

Although no official announcement had been made by that stage, Branch's departure had been confirmed by Steve Cotterill in interviews leading up to this testimonial match.