The British book we turn to first for help in minding the gap between your terms and our terms, Cooks' Ingredients, says what we call coarse cornmeal, you call polenta or maize meal. Finely ground cornmeal, it says, we just call cornmeal, but you call maize flour. (We actually often call finely ground cornmeal corn flour, but that creates confusion with your corn flour (see below).

Darina Allen, founder of the Balleymoe Cookery School in Ireland, refers to polenta flour or simply polenta as the name for coarse cornmeal. In this country, we know polenta almost exclusively as the finished dish and not as its main ingredient.

Alan Davidson, author (British) of The Oxford Companion to Food, just refers to cornmeal (although he does so only in the section on maize, not corn, which makes it hard for us over here to find).

So the choice is yours - cornmeal, maize meal, maize flour, polenta, or polenta flour. Our search on the Tesco supermarket Web site, however, turned up a response only to the term "cornmeal." It offers two versions - coarsely ground or finely ground - and although the search won't find it, the package also refers to the product as polenta.

Now, what you call cornflour, we call cornstarch, and it is something else again. Unlike cornmeal, which is milled from the whole kernel, cornstarch/corn flour is milled only from the endosperm (the outer part) of the kernel. It is used primarily as a thickening agent, and, in combination with wheat flour, in baking. It is used much more in baking on your side of the Atlantic than ours.

And finally, we hope you will notice that we did not use a bit of sarcasm (what we - perhaps mistakenly - call wit) in this answer, having recently been taken to task for the sarcasm apparently dripping all over our British-American flour primer (and which we finally had to modify, because we were apparently mean-spirited and not funny at all. Sigh).