1930 British Empire Games

At the inaugural British Empire Games in 1930 in Hamilton, Ontario Burleigh, aged 16, became the youngest swimmer to represent Canada.^[3] He won bronze in both the 440 yard freestyle and 1500 yard freestyle events.^[4][5] He also won gold, along with teammates Munroe Bourne, Bert Gibson, and Jimmy Thompson, in the 800 yard (4 x 200 yard) freestyle relay.^[6] Only two teams entered this event, with England winning silver, only 2 yards and 0.4 seconds behind Canada's time of 8 minutes and 42.4 seconds.^[7][8]

1934 British Empire Games

At the 1934 British Empire Games in London Burleigh won three gold medals, later describing it as "my finest hour".^[1] 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).^{[1][9][10][11]} A new games record was set in all three events.^[9][10][11]

1938 British Empire Games

The 1938 British Empire Games in Sydney was Burleigh's last major competition.^[1] The Canadian team travelled from Vancouver, with stops at Honolulu, Fiji, and New Zealand, where the team took part in exhibition meets.^[1]

In the 880 yard (4 x 220 yards) freestyle relay Burleigh, along with teammates Gordon Devlin, Robert Hooper, and Bob Pirie, won silver.^[12] He also competed in the 110 yard freestyle competition but was not placed.^[13] The gold medal was won by fellow Canadian Bob Pirie.^[13]