Wrong Tpl. The same 1931 Statute of Westminster that gave Canada independence replaced the British Empire with the British Commonwealth, consisting of the Britain and its colonies, as well as the Dominions of Canada, South Africa, Australia, New Zealand, and Newfoundland. By 1934 Newfoundland had reverted to being a British colony.
This meant that Commonwealth forces fought the war under one command (apart from the Aussies And New Zealanders, who set up their own commands when their homelands were under threat of invasion). Not Empire forces.