Do you consider chicken tikka masala to be Indian or British cuisine?!
Even though it was inspired by Indian cuisine, it's not "real" Indian food.
Answers:
The food that's served in Indian restaurants is Indian food served in a very British way. Chicken tikka is Indian and masala is Indian, but they're not usually combined together in India. However, the British traditionally liked to have some kind of sauce or gravy on their meat, so when they were in India (or hiring Indian people to cook for them) they asked for some kind of sauce with the chicken. So while tikka masala is not a traditionally Indian dish, the parts that make it up ARE actually Indian. They're just put together very Britishly.