I’m pretty certain that Britian would lose. Are the US and USSR allies, cause in that case the Home Islands are probably going to be overrun and a British Government in Exile might be set up in Australia. If the US and USSR are rivals, and if the British, for some reason, just totally stayed out of WWII.... maybe after this US invaded Canada, the British Empire restructured itself somehow (more likely it was collapse, but we’ll assume it didn’t). With the entire Empire having a say in the matter, this ‘new’ ‘British’ Empire stays out of WWII (still not sure how the Soviets can beat Germany single handily but whatever). Anyway, the Soviets are overextended and war weary, the Americans had to fight Japan (and because they are seemingly evil ITTL) they annexed the former Japenese Empire, so they are similarly war weary. We’ll go ahead and say that all the German scientists fled to England, so the British have developed nuclear weapons, and the US had to invade the Japanese Home Islands. Assuming all that this alt ‘Britian’ can leverage its nuclear capabilities (short-term advantage, the others will develop them soon) with his democracy and free market which will allow it to perform better economically and scientifically (long-term advantage). However both rivals have far higher populations which will put Britian at an enormous disadvantage.