During World War II, the Commonwealth air force units primarily consisted of the Article XV squadrons, which were part of the British Commonwealth Air Training Plan (BCATP). These squadrons included Australian, Canadian, and New Zealand air force units formed from graduates of the plan. The BCATP was a large-scale multinational military aircrew training program established by the United Kingdom, Canada, Australia, and New Zealand to train pilots and aircrew from different Commonwealth countries.
For more details, you can check the Wikipedia article on Article XV squadrons.