Paneer certainly existed before the British came to India and has long been a part of Indian culture. However, there is some controversy as to it's origins. The etymology of paneer is Persian, and according to some paneer was introduced to India during the Muslim invasions of the late middle ages. However, the Vedas and other later examples suggest Indians might have been eating something very similar to paneer well before that. However it's hard to know if they were referring to what we consider paneer, or some other dairy products.