How much authority does London have over the Dominions? What, politically, ties the Empire together at this point?
So, for GB, Ireland and the Dominions, they are in a real union, which means they share a foreign and defence policy and are in currency and customs unions with each other. As regards who still calls the shots on those policies, London still has a kind of primus inter pares status but that’s going to be eroded over time especially with the rise of India.
Also, the Dominions all share a single Royal Navy and Imperial Army, which I will elaborate on in a future post.
As regards the non-Dominion bits of the empire, the colonies in Asia and the Caribbean are basically as OTL. In Africa, the model is to pursue protectorates along the lines of OTL Egypt and Botswana rather than Crown Colonies but to an extent that’s an academic difference.