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Barry, your post 2 implies that it would be better to have the British Empire. It wouldn't!
In the 18 hundreds, many African tribes received a protectorate status from Britain, sometimes in return for mining rights. Similarly, many local Indian leaders of independent states in India received a similar status. Only gradually did all this evolve into an Empire, I think it was Disraeli who became the architect of the term British Empire as we know it to be. The actual areas that British people, and Irish people, settled in as British governed territory, are the original thirteen states of the USA, and Canada, Australia and New Zealand, and also South Africa and Zimbabwe (Rhodesia).
It would be feasible to have a special relationship with Canada, Australia and New Zealand, but all the other countries are independent, with age-old civilisations, and have plenty of people of their own to govern themselves.