Queeley played for England at the 2015 FIBA Europe Under-16 Championship in Kaunas, averaging 3.5 points per game in a limited role. At the 2016 FIBA U16 European Championship Division B in Sofia, he averaged 12.2 points, seven rebounds and 2.5 assists per game and leading England to fifth place. Queeley represented Great Britain at the 2018 FIBA U18 European Championship in Latvia, averaging 12.4 points, 4.7 rebounds and three assists per game. At the 2019 FIBA U20 European Championship in Tel Aviv, he averaged 12.3 points and four rebounds per game for Great Britain.