The time line broke way before the 70's and it broke due to the arms race not stopping after the end of WWII...
I highly doubt that in such an intense arms race Britain would let go of Canada...
Also I seriosely am backing the View that Britain would have survived, whether Britian home soil survived or just part of their vast empire, or even just a few ships from thier navy...
I belive they would have had one of the four largest armies in the war.
Chinese, Russians, Americans, British Empire.
And I belive the British would be the most prodominantly naval and also the most spread out.
Meaning they had optimum chance to survive...
What happened to Her navy? Old boy, it is the British EMPIRE for a reason! Her Majesty is always in firm control of HER ships, sir!
Anyways... As it has been repeated over and over, the Resource Wars saw Europe fragment, that would have most certainly included Canada, which have made them very weak to a US invasion, in fact I would almost stipulate that perhaps many within Canada would have seen an American annexation preferable to chaos that a weak and ineffectual government would have given them. As for the British, I doubt they would have fared much better than the rest of Europe since they were a confirmed member of the European Commonwealth they were already losing a majority of their resources helping build a huge navy for the rest of Europe and fighting to hold on to the Middle East, they would have lost some of their colonial navy and army in Israel.
Mind you, the British have been equaled at sea before when it came to Germany, how can you just ignore the battle of Jutland or the German battleship Bismarck, and France, which was able to at least go toe to toe with British ships on a regular basis.
I could even make the argument, that with their superior resources of uranium and ore, that it would be the French who would have had a much better chance of surviving the wars. In fact I would find it hilarious to find a French Sub in Quebec City or somewhere in North Carolina much like the Shi Empire, they try to create a Creole Empire mixing their French with a Southern English accent.