Question

Which was one of the first territories to be annexed by british

Answer 1

It was Awadh..
....
Got it

Answer 2

After coming to India, the British became powerful after Aurangzeb's death. When the French came to India, they won against the French in the Carnatic Wars. The Northern Circars, a part of the Carnatic region, came under British control and they gained more influence over the entire region.

So I think it is the Carnatic region.