In England there is no special kind of bread for toasting, as in Germany; the kind of bread most people eat normally is suitable for toasting, but we'd just call it a square, white loaf (or a square brown loaf). We also cut baguettes into slices and toast that, for example. This basic kind of bread you get in the supermarket comes in various varieties (wholemeal, multi-grain, white, malted, soya, granary, sunflower seed, etc). Most people buy those as you can use them to make sandwiches easily.
(In England we make sandwiches with two slices of bread and a filling, which means that thick, hard, dry bread is not very suitable and the thin, soft sort you get in packets - which you called Toastbrot - is just right. In Germany you make open-top sandwiches so you need a thick kind of bread which will not bend when you lift it.)
If you go to a decent supermarket or baker's you can also get bread in loaves which are not square or pre-sliced, for example rye bread, olive bread, sourdough, baguettes, ciabatta, herb bread, walnut bread etc. However, if there was ever a tradition of regional specialities this has more or less died out in Britain.