Why does a back boiler make a knocking noise that keeps me up all night?

I take it you are from UK. If it is a back boiler type heating system then it could be very old. If the boiler is knocking then it is most probably all furred up. Have you asked your neighbours if they could shut it off at night? It must be disturbing them also. Just keep asking them and the Landlord and if you get nowhere then go to the noise abatement people at your local council. Good luck.