Yes you can claim, you are covered under the law of TORT, as the injured party it does not matter whether your vehicle was insured or not, or even road legal. Should the vehicle cost a "sum" of money to repair the damage caused, you are entitled to make a claim to recover this "financial" loss. Your entitlements under a third party fault claim are here . fenchurchlaw.co.uk/coles-v-hetherton-implications-.../

You can either deal with the third party insurance company directly, have a solicitor deal with it directly on your behalf, or go through an FCA regulated claims management company to arrange repairs and pursue your financial loss. Should you deal with the third party insurer directly, things may get resolved quicker, though should anything go wrong, you have no entitlement to arbitration through the Financial Ombudsman Service. Should you go through the other two options and something goes wrong, you have the entitlement to go through the Legal Ombudsman. This affords you better protection. And you are not responsible in any way.