It's strange you should say that, as Britain has already controlled the vast majority of Canada - even all those empty islands in the north.
Actually the Canada you controlled was a colony the size of 4 present day Provinces. You didn't control any land past present day Ontario. Furthermore your "control" over Canada was anything but. Yes you were seen as the rulers of the colony, however numerous First Nations tribes had full run of their land, despite Colonial Law prohibiting it. Also you had next to little control of the borders of said colony, as can be highlighted by the Fenian Raids, in which the Irish Republican Army (the true IRA of the 1800's) captured Fort Erie. In fact, if you back track throughout the history of Canada from Colony to Dominion, a huge part of the defence of said region was played the local militia, Canadians. An excellent example of this is the Battle of Chrysler's Farm, in which 7,000 men of the U.S. Army were soundly defeated by 800 Canadian Colonial Militia and Native Scouts with support from a handful of British Skirmishers and a British Artillery Battery. As I stated above, yes Britain ruled Canada, but your control over it was flimsy at best.
With all that said, given the differences in the World today as opposed to the 18th and 19th centuries, one cannot deem that Britains rule of Canada could be repeated today. First and foremost there is the fact that present day Canada is
MUCH large than the small parcel of land known as Upper and Lower Canada was. Secondly there are thousands upon thousands of population centres in Canada today, there were but a few dozen during the colonial period. These centres would require troop garrisons to control. How many troops do you think it would take to subjugate the major Canadian centres; Toronto, Montreal, Vancouver, Ottawa, Edmonton, Calgary, etc? Putting a rifle company of redcoats in to the town of Hull in the 1800's cannot be likend to having to place the 2nd U.K. Armoured Division in to Toronto in 2006. While I know this is all guess work, and completely far fetched, i'm merely making it a point that no nation, not even China, could waltz in to Canada and control the nation in every sense of the word. It is too large, and too far flung for that to ever happen. As for my references to the past, that was an educational lesson on the short comings of the British Colonial Defence of Canada until the formation of the Dominion. It was flawed and more often than not inadequate for the job. My 43 cents.
