Sure, I may swear my allegiance to the queen, but to me she's the queen of canada, Don't forget that for 2 years we were the only country in any position to help you out, and we were the one country that sent supplies during the battle of Britain. Sure the americans could out produce us, but on a per capita basis we were one of the highest producing country.
Also 40% of the male population that was eligible to enlist, had enlisted, and 1/10 of the population was actively enlisted in the army.
With another 1/3 of the population directly involved in military industry.
You wouldn't be around if it was for us braving the oceans of u-boats to save your ass.