Two very general comments:
1) Time frame. The Dutch got there first for a reason, which I believe is that the Dutch East India Company was operational a generation before Britain was in a good position to be operating in the region of southern Africa, due to the nature of Charles I reign and the subsequent English Civil War. Preempting the Dutch with English settlement is going to require a reason why the English were more capable than the Dutch regionally at the time of or before OTL Dutch claiming and effective control of the Cape. Or it might be possible for the British to leapfrog past an established Cape colony to Natal or something like that, but then the two would be rivaling each other at close range.
2) the success of the Plymouth colony in particular was due largely to a major plague having wiped out the Massachusetts coastal Native people, leaving towns and fields pre-developed for the Puritans to appropriate; Squanto's presence as an advisor was also helpful. Similar opportunities, not quite so one-sided, but giving the English opportunity for easily lodging themselves without too strong Native opposition were important in Virginia earlier too I believe. And in general, Native Americans suffered in their attempts to oppose settlement when English numbers were weak because of their vulnerability to disease. Even so, the colonies despite their proliferating numbers and populations were in a precarious position versus Native resistance at least until the early 18th century. We can look back and say that given ongoing support and emigration from Britain, the outcome was inevitable, but it seemed very "evitable" at the time! Indeed serious worries about Native power to resist, given some organization and ready access to firearms, was a serious concern well into the 19th century; the War of 1812 was mainly about fear that Britain could block American expansion westward via arming and organizing the Indian tribes. Therefore the factor of Native demographic vulnerability to massive die offs due to Eurasian diseases was tremendous in the success of BNA and subsequent USA.
Whereas a colony in South Africa faced Native resistance by Natives who were not nearly so vulnerable; to advance in face of them meant either extermination in combat and subsequent deliberate massacre, or subordination of the Native people under colonist authority in one way or another. The advantages of Early Modern weaponry versus various Native kits around the world were not so tremendous in centuries before the mid-19th; development of weapons such as the Maxim Gun infamously turned the tide. Before that, there is no doubt that very well supplied and organized European forces could indeed outfight larger Native ones, but the balance was much closer, more so in Africa against people like the Zulu who had iron weapons than in North America--even so, in America the Natives were hardly overawed by firearms or other European tech; they could accomplish quite a lot against armored and musket-armed English with arrows, canoes and their usual tactics.
Cape Colony in fact remained initially tightly under the control of the Company OTL; eventually exasperated colonists would curse the Company and move out of range of its short-armed control, but not too far, well within the modern Cape Colony boundaries. It helped that the major warrior peoples of southern Africa were farther west and themselves recent migrants into the region, and that locally they were up against only gatherer-hunter peoples whom they could subjugate easily.
But the point here is that even with a much more expansive demographic base, with a colonizing regime more interested in expansion than in merely maintaining a single strategic seaport, an English colony would have run into a desert in one direction and some really tough Native resistance in the other. The Zulu and other Bantu peoples would not perhaps be a lot more effective, man for man, than the Native Americans--but they would be found in much larger numbers, numbers that do not vanish "mysteriously" or "providentially" upon first contact but persist unless cut back the hard way.
This second point does not stand in the way of England/Britain establishing and holding an early and securely held Cape Colony, but if someone is thinking an African "Virginia" or "Plymouth" will turn into a white-majority British Southern Africa or US of Africa running up to the fever zones, with southern African natives meeting the same fate that eastern North American ones did, that would be much mistaken. Expansion, especially onto good land, would turn into a slow slog, and given that even defeated African peoples would live on tenaciously a successful English hegemony would almost certainly take a form similar to OTL in the region--which is to say, a small "white" minority ruling over a subjugated but demographically overwhelming majority African population, with a large number of mixed-race people between or socially off to the side. The exact form of racist confrontation SA presented OTL might differ somewhat; conceivably mixed-blood people might be recruited as subaltern but moderately privileged agents of the order instead of shoved to the side as some kind of embarrassment, for instance. But by and large it will be far more difficult for settler descended populations to expand and fill the continent than in North America. British cultural and social success there would be much more a matter of inviting and welcoming African peoples into it and reconfiguring their values to be British; if the color bar is set up as a matter of a privileging hierarchy of any kind, the inevitable result is resistance and limitation--or conceivably, a really terrible instance of genocide perhaps. One quite liable to backfire and turn into a fanatical drive to extirpate Europeans, or anyway Anglo-Europeans, from the continent completely.