He joined Swindon Town after the war, where he made his Football League debut in the 1947–48 season.
Born in Deptford, London, Nunn's playing career began with Bexleyheath and Welling.
Immediately before the outbreak of World War II, Nunn was signed to Charlton Athletic, but he made no first-team appearances for the club.
He made his Football League debut during the 1947–48 season, going on the make a further three appearances across the campaign.
Ahead of the 1948–49 season, Colchester United manager Jimmy Allen brought Nunn to the Southern League club,[1] making his debut on 21 August 1948 in a 1–1 draw at Cheltenham Town.