Note: edited based on helpful comments.
In Walking with Cavemen, Robert Winston claims an African rainforest existed 8 mya, but by 4 mya it was gone. He attributes this to newly Himalayas-triggered Indian monsoons, which prevented rainfall from reaching Africa. However, it's my understanding that India collided with the rest of Asia circa 50 mya. So why did the monsoons take so long?
Multiple comments have noted that Winston should have credited the monsoons to the Tibetan plateau. Either way my assumption is that, until the mountains had been pushed up far enough, they didn't threaten the forest's rain supply. On a linear approximation, by 8 mya the Himalayas' mean height would be approximately 85% of its present value, which bounds the "critical value" of the altitude as a percentage of its current one. A similar calculation applies for the Tibetan case.
Why did the motion of India lead to a multi-stage mountain formation? How did the timing of these effects influence Africa?