Britain loses the ARW worse so that loyalist refugees are forced to flee to South Africa rather than Canada and set up a highly efficient slave based economy. (Sorry
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Somewhat more seriously, as has already been mentioned a South Africa that avoids apartheid is probably the best bet. As to how to achieve it - more British immigration in the 19thC so the Afrikaners never get a majority would help, so would a slightly more enlighted native policy so that major groups like the Zulu and Xhosa preserve their independence (Swaziland or Lesotho style) under British protection so South Africa doesn't have to put so much time and effort into keeping them down. Maybe throw in some more British colonies in the region (the Rhodesias, Nyasaland) into a federal state and add in some other random bits and pieces such as St Helena and Tristan da Cunha to meet the overseas territories arrangement and you should at an absolute minimum have a country that is the most powerful in the southern hemisphere.
Somewhat more seriously, as has already been mentioned a South Africa that avoids apartheid is probably the best bet. As to how to achieve it - more British immigration in the 19thC so the Afrikaners never get a majority would help, so would a slightly more enlighted native policy so that major groups like the Zulu and Xhosa preserve their independence (Swaziland or Lesotho style) under British protection so South Africa doesn't have to put so much time and effort into keeping them down. Maybe throw in some more British colonies in the region (the Rhodesias, Nyasaland) into a federal state and add in some other random bits and pieces such as St Helena and Tristan da Cunha to meet the overseas territories arrangement and you should at an absolute minimum have a country that is the most powerful in the southern hemisphere.