Interesting comments all around here.
G, to answer your question: Up until fairly recently, our passports referred to Canadians as British subjects. I suspect since the repatriation of our constitution from UK in 1982, this has now gone by the wayside, although of course the Queen is still our head of state, to wit, Prince Charles being here now.
As we did not have extensive offshore diplomatic missions until post WW2, the Brits taking care of the majority of our external affairs, and since we were technically British subjects, although a self-governing dominion, we simply referred to ourselves as British when travelling offshore to benefit from any international protection we might need from British consular offices. Although we are now much more viable on the international scene, it is still recommended that we seek assistance from the British consular offices where no Canadian one can be found.
And, of course, as S says, outside Quebec, the vast majority of Canadians at the time were of British stock. We were quite content to let Mother England look after our affairs.
I hope this helps.
G