 He played for Swinton during their two successive Rugby Football League Championship winning seasons; 1962–63 season and 1963–64 season, where he often scored, or created tries with his blistering burst of pace when going at defenders.Many Lions fans believe he was the finest Swinton of the post-war era when he wore the famous blue jersey for Swinton at their famous Station Road stadium, scene of many big matches - Test matches, Challenge Cup semi-finals, Lancashire County Cup finals and Championship finals during the period from the 1930s to the 1980s.Graham Williams then moved to Australia, joining North Sydney, and then Manly.