It's a trope for sure, but it doesn't really make sense: a lot of American dishes are traditional British foods. Roast dinners with stuffing and gravy, apple pie, pancakes, biscuits/scones, fried fish and potatoes, meat pies. Thanksgiving dinner is an ancient British harvest feast with some New World ingredients; Christmas dinner is the same format.

And since most American food has also made its way to the UK, there's really not a great deal of difference.