While he made his name as guitar player for Blur, Graham has also played saxophone and drums on many Blur tracks. He composed 1997's "You're So Great," as well as much of the band's 1999 hit single "Coffee & TV," which he also sang. More recently, Graham produced (alongside Stephen Street) Blur's 2015 album The Magic Whip, which debuted at #1 in the UK album chart.

Graham has released eight solo albums:
The Sky is Too High (1998), The Golden D (2000), Crow Sit On Blood Tree (2001), The Kiss Of Morning (2002), Happiness In Magazines (2004), Love Travels At Illegal Speeds (2006), The Spinning Top (2009) and A+E (2012), as well as the Original Score for the BAFTA Nominated Netflix series 'The End of the F**king World' in 2018.

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