I think, like some Chinese food, the differences in style of Indian might be down to which area of India people have immigrated from.
We had a large Indian community in Johnstown PA and they did a food night quite often. I enjoyed the food, but it wasn't like "British" Indian. But they were from India, they were cooking mainly for other Indians in the area, so no reason for it not to be authentic.
They had never heard of Chicken Tikka, because that is a British dish and I loved it.