"While the Canadians" may not always require the definite article, there are over 10,000 written instances showing they're quite capable of taking it on board.
We British, on the other hand, can only do without it in constructions like that (where "We..." effectively stands in for "We, the...").
It's probably connected to the fact that we have an alternative demonym that doesn't normally take a definite article...
"Americans, Canadians, and Britons" are all anglophones.
(as are "The Americans, the Canadians, and the British")
Per MετάEd's comment to the question itself, the British normally refers collectively to a people, so you'll see things like The British are an industrious race. But in contexts where multiple individuals are being referenced, we'd normally say something like Four Britons were among the dead.
It's interesting to consider the position of the French here. Several French were among them is really unusual (that was the only clear-cut example I could easily find in Google Books), whereas two Frenchmen were among [them] is unexceptional. I don't know what the disaster reporters would write if the French casualties were a man and a woman, but not actually a French couple.