Graham was born in the Southdene district of Kirkby in Lancashire, a satellite town of Liverpool, to a paediatric nurse mother and a social worker father. His paternal grandfather was Jamaican and one of his grandmothers was Swedish. He has portrayed characters from several British, Irish and American regions, including Cockney, a Geordie, a Liverpudlian, and a Scotsman; an Irish gang member in 19th-century New York City, a 1930s Chicago bank robber, a Brooklyn mobster, a Texan, and the short-fused English nationalist, "Combo", in This Is England. He was nominated for an RTS Award for his work in The Street and a British Independent Film Award for his work on This Is England.