Where in England did you visit? You might find some places more dense with foreign people than others. If in London, then you're looking at a large mix of cultures. Though my town has a strong Eastern European population, but they're still a minority group, despite what some people like to believe.
Foreign food is actually quite popular here, so I can imagine a foreigner coming to try the British cuisine might be a bit limited for choice in restaurants and cafes.
You'll normally find things like roast dinners, lamb joint, pies (like Steak and Ale), steak dishes and fish n chips - I know Wetherspoons do dishes like those (they're a chain of bar/restaurants around the country) - their menus try to offer some variety - you'll also get lasagnes, curries, chillies, burgers and the like. If you find a tea shop then you can have tea and scones and feel like a British stereotype.
Our house tends to have quite a mix of food, we still eat plenty of different British dishes, but we also eat a lot of foreign food.
And of course, yes, we pretty much tried to take over the world once upon a time, it's quite possible the British empire has brought some influence to our cuisine, well, you can blame the British Empire for our obsession with tea.
But we've had influxes of people coming here since we became weaklings. We have a strong Asian community and it might be responsible for the reason we enjoy Asian food instead of the Empire's colonisation of India.
The current complaint you'll find is eastern Europeans, but we adopted the open border policy of the EU, so we don't have as much border control as we used to. Not that I mind people immigrating over, it brings a nice variety of culture and some are quite interesting people, but obviously some would argue we've over done it and wonder if it's good for our economy.