score:10
First of all, both India and South Africa became free of Britain, shortly after World War II, India in 1947, and South Africa in 1948.
Your question appears to be, why didn't "indigenous" people in South Africa become free at the same time as the Indians.
The answer is that there was a large white minority in South Africa (about 25% of the population) in South Africa, who held a disproportionate share of the wealth and power. Within this "minority," the British were only second; the larger group was a Dutch-descended group called the Boers. Moreover, the non-white 75% was split into three distinct groups, Africans, Indians, and "Coloureds," people of "mixed" backgrounds, with the Africans further subdivided into different tribes.
The Boers filled the power vacuum left by the British. It was not until 1994 that Nelson Mandela managed to enforce the principle of "one person one vote," that gave the black majority (theoretically) equal rights with the whites.
In no other former British colony was there such a large European minority that retained "colonial" power after the British left. Put another way, there was a second white "layer" that retained power after the colony became independent of Britain.
Upvote:11
Following up on Tom's answer, there is actually a reason there was a large white minority in South Africa, but not in India.
The Bantu peoples (of which most living native South Africans are descendents) spread across most of Sub-Saharan Africa in large part due to having an agricultural package that worked well for that tropical climate. In particular, millet and sorghum. Indian agriculture was heavily reliant on tropical/subtropical rice and millet crops. European agriculture was heavily reliant on temperate and Mediterranean crops like wheat and barley. Keeping that in mind, look at the world climate map below:
You may notice here that, while India is all tropical and subtropical, South Africa has a lot of Steppe, savannah, and a strip of Mediterranean climate on the south coast. These areas, particularly the southern coast area, are not places where millet and sorghum grow well. That explains why those areas were relatively lighter populated when Europeans arrived; if you can't grow crops there, you can't support the population density associated with an agricultural (rather than herding or hunter-gatherer) society. The fact that their crops grew great there explains why the Europeans themselves found it a great place to emigrate to, and thrived there.