At the 1934 British Empire Games in London Burleigh won three gold medals, later describing it as "my finest hour". Burleigh won individually in the 100 yard freestyle event, and as anchor in the 330 yard (3 x 110 yards) medley relay (with Ben Gazell and Bill Puddy) and the 800 yard (4 x 200 yards) freestyle relay (with George Larson, Robert Hooper, and Bob Pirie). A new games record was set in all three events.