Yes. It will. Almost any thickness of insulation makes a big difference. There is a law of diminishing returns which means that the first few centimetres make all the difference.
Yes. I'd put sheet plastic on the outside of the insulation to prevent penetrating damp and line the inside with vapour check plasterboard (i.e. foil stuff with taped joins). Otherwise, just use plastic sheet and chipboard on the inside. Also, consider using expanded polystyrene sheet instead of Celotex. It isn't as good at insulating, but is much cheaper. Obviously, if there is particular fire risk, you may need to take this into consideration.
Christian.