No you dont have to leave Holland by the date it expires. You as holder of a UK passport have a right to live in any country in the EU. Your right does not vanish because your passport has expired. You do not stop being British when your passport expires. Local dutch laws may require everyone to be in possession of a valid document, however i dont think that is the case. You may need it renewed if you are travelling out by air. But you definetly do not have to leave the country before it expires.