What word do British people typically use for "apartment"?

The corresponding word in British English for apartment is flat. The name is an alteration of the now-obsolete Scottish noun flet, meaning "floor" or "ground under one's feet." In the 19th century, flat came to be used as a variant for flet and additionally gained popularity as a word to denote a story of a house or building, and then a multi-room apartment situated on one floor.

Source: Merriam-Webster