Americans say 'apartment' when we would say 'flat'. .
It's misplaced snobbery and fashion in Britain to refer to a flat as an apartment. Truly rich or aristocratic British people still refer to their flat as a flat. Estate agents of class call them flats too, unless they are hoping to sell to Americans or other foreigners . Flat in American has a bad connotation and in other languages e.g French, the word apartment is readily understood (In French, for example, it is 'appartement')