Eh, to some extent, but we've got the foresight to accept these dishes as being British when you consider that the foods we eat aren't authentic to those areas. Spag Bol isn't being eaten in Italy, nor is Chicken Vindaloo in India.

We've got a long enough history that we can trace back when the Normans and Saxons came here, alongside the culture changes of Indian settlers, Jamaican workers, Irish, etc. That acceptance is not only why there're a lot of distinctly British versions of different cultures' food, but why many cities in the UK also serve decidedly authentic food at some of the best restaurants in the world - and that doesn't even factor in how some cultures have fused over time.