Just to clarify the "Armoured/Tank" designation of Commonwealth troops:
Two main arms of service are Infantry and Armoured. Historically, most Armoured regiments are descended from Cavalry, hence the nomenclature 'regiment' for a battalion-sized unit, and the smaller formations called squadrons, troops and patrols. Incidentally, a private from a Cavalry unit is the only soldier properly called 'Trooper.'
Infantry units that are equipped with tanks are referred to as 'Tank,' because they're not part of the Armoured Corps. Conversely, armoured units may have a substantial infantry component.
My knowledge of WWII military history isn't great, so correct me if I'm wrong.