Let's remember a few points when we talk about apartheid in these territories. The Cape Province's black population was small until the 1970s and 1980s, when blacks started migrating there looking for work. The Cape in this scenario would probably have a white plurality, with mixed-race/colored people being much of the rest. This would make apartheid pretty much irrelevant, because there is so few black people.
Natal is the one in big trouble. You got two of the biggest tribes in Africa (Zulu and Xhosa) there, and then you also have the Indian population. The result there is a tinderbox waiting to go off, because the territory's population would be overwhelmingly against the white rulers, and if Natal is on its own, that means much of the wealth of South Africa's awesomely mineral-rich interior doesn't make it out.
The Free State and the Transvaal have the vast riches, but the British will still want to have them for themselves, though the Afrikaners will still want their share of the pie and they will undoubtedly get it eventually. They will be outnumbered by the tribes in that part of South Africa, too, and the diamond mines, don't forget, are mostly in the Cape Province.
A union between all of them would be pretty much inevitable, if for no other reason than to save Natal from becoming a war zone. Plus, we all know that Britain was always very happy to do arbitrary integrations of colonies into larger countries, and they did just that with Rhodesia, among others.