Whenever someone damages your property (either through a deliberate action or through negligence) you have the right to claim compensation from them. If they've got insurance in place they can pass the claim on to their insurer; otherwise they must foot the bill themselves. (i.e. the absence of insurance doesn't prevent the person who has suffered loss from demanding compensation).
If you can put a figure on the damage which has been caused to your property (e.g. by getting several quotations for remedial work) you should send a written demand for compensation to your neighbour. (I recommend sending it by recorded delivery, even though its only going next door, as a court might require you to prove that you made the demand). The demand must show your name and address, and that of your neighbour. It must be dated and clearly state the amount demanded, and the reason why. It should also state that if payment in full is not received within a specified period (I suggest 28 days) you will commence legal action.
http://www.smallclaim..._forms/ex301_0406.pdf
http://www.smallclaim..._forms/ex302_0406.pdf
Chris