Just to add to this, завтраком is in instrumental case (за́втрак is masculine); and за + instrumental case means at/while or behind/beyond (physical location).
I'm a native, educated British English speaker and regularly say to my neighbour "have you time for a cuppa?" She may sometimes answer " Sorry, I haven't time". The latter was marked as incorrect on one of the exercises. This answer would be acceptable in British English.