You may be able to keep paying the �80 to the council just to reduce the amount, and they MAY be willing to notify the bailiffs of new balance each time. This doesn't necessarily mean the action will stop though.
If you cannot afford what the bailiffs are asking, you could always just ignore them whenever they call which would mean the case will go back to the council, and you may be able to come to another agreement then.
Strictly speaking, if you owe money after a Liability Order is granted then they can take further action, even if payments are coming in.