(2-part post):
There are two ways of reading your question. Firstly you could be asking about what types of food feature among British 'speciality dishes' (but which, in reality very few Brits actually eat on a regular basis) or you could be asking about what we actually eat.
When I met someone from the USA (who I'd originally encountered here on AB) a couple of years ago, I consulted the website of his home town (Lake City, Colorado) to try to learn something about where he lives. I was surprised to see that the only eating establishments listed were just offering steaks and burgers, etc (with just one fish restaurant opening on a seasonal basis). In the UK we tend to have more cosmopolitan tastes. In the small town where I live (with a population of under 5000) there are two takeaway establishments serving Chinese food, plus one serving Indian food and another (with 'eat in' facilities) serving mainly Italian dishes. There are also two traditional fish and chip shops (which sell things like meat pies and chicken, as well as battered fish). Further, there are two restaurants modelled on the idea of traditional English tea rooms, but both of these serve things like Thai curries alongside more traditional dishes, such as roast beef with Yorkshire pudding and vegetables. The 5 pubs all serve food as well. In all of them you'll be offered a variety of curries, pizzas and pasta dishes (among many other dishes), as well as British favourites, such as fish and chips, steak & kidney pie, cottage pie, roast beef, casseroles, stews, etc.