More likely that the UK government moves to Canada and continues from there, I don’t think Canada would have fought on independently if Britain had officially surrendered.
Not so much surrendered, as got it’s but kicked in a G2 Sea lion. I got this rule from another thread stating exactly what you had mentioned, but I found that Britain wasn’t as crippled as it should have been once it lost London, at least this way, we Canadians get our Canada in the game AND Germany can still open the door to Africa for their little Italian buddy.