India was one of the wealthiest regions on Earth into the 18th C, and had developed cash crop systems along with cottage industries and a massive labour force. Initial British (and other European) involvement in India was to try to control the extremely lucrative and already established cotton cloth trade, along with other developed resources and cottage industries such as jute, saltpetre, spices, indigo etc. In contrast, any such cash crop complex in Africa would have to be developed from scratch and would rely on a much smaller working population.

I'm linking here to Trade, Labour, and Transformation of Community in Asia which details the economy of Bengal in particular, although such factors were also present elsewhere in India to lesser degrees.

Basically it's more effective to take control of an existing market than to develop one from scratch.

I can't speak about Africa, but I can help you get a better idea of South Asia's importance to the British and why they had a vested interest in having influence there.

The British had a lot of economic incentives to focus on India, for reasons that Flocculencio wrote about. These became quite strongly tied to political incentives in the mid 18th century during conflicts between the French and British, i.e. the War of Austrian Succession and the Seven Years War. These initially bled over from Europe into South India where the British and French East India Companies both had trading bases, the British in Madras (now called Chennai) and the French in Pondicherry. (Here's a map so you can see the relative positions of the cities- they're not extremely far away.)

Now in the 18th century, the British East India Company was still privately owned, unlike the French one that was largely controlled by their government, though the British government was still willing to invest troops in protecting their trading interests. The French Governor-General of India at the time was also interested in using his Company's power to expand French influence and territory in India, a wish threatened by the presence and strength of the British (and one which the British eventually felt threatened by.) This turned into a situation where the French and the British were willing to fight to extricate the influence of the other from South Asia, and kicked off what are called the Carnatic Wars. They eventually involved both powers involving themselves in local politics and exploiting political situations to strengthen their own positions and influence, and ended with the French being effectively neutralized as a power not just in South India, but in South Asia as a whole. This left British interests in a very strong position, and directly lead to them essentially becoming a political power with tax-collecting authority over Bengal and surrounding areas.

So to sum up and help you with your question, the British ended up becoming more powerful in India before Africa because it was advantageous at the time for them to expand and defend their interests against the French, with whom they were in direct and urgent competition due to conflicts in Europe.