When someone, through negligence, harms you or your property, you have the right to demand compensation from that person. An insurance policy allows someone to pass the bill on but the absence of insurance doesn't mean that the wrong-doer escapes the liability to pay compensation.
If the uninsured driver has got any form of capital (e.g. a house or a decent car) speak to a solicitor about suing him. (There are plenty of 'no win, no fee' deals around but check the small print before entering into any agreement). You might be able to force the guy to sell his house (for example) in order to provide you with some compensation.
Chris