In The Man in the High Castle, an alternate history novel read by the characters has as its premise a world in which the Axis is defeated, only to have a Cold War develop afterwards between a progressive USA (which solves its racial problems by the 1950s) allied with a Republic of China, and a surviving British Empire (which, in addition to its OTL territory, dominates Europe), which ends with Britain overtaking the USA to become the world's hyperpower.
Now, recognizing the implausible aspects of TGLH world (a senile Churchill lording over a racist Empire into the '60s, ect.) how could we get a situation that, by the 1950s, has the USA and China facing off against the British Empire in a cold war? Which bloc would ultimately prevail in such a situation?
The POD can be anytime from 1900 onwards.