Hi Bekky
Usually it would be quite easy to get compensation from such circumstances, given your situation although the driver was not insured teh vehicle may well have been and dependant on the circumstances the insurers may well act as "relevant RTA insurers" they may put up a fight but thr right solicitor will get this for you, alternatively you can claim via the Motor Insurers Bureau however they will only pay a nominal amount towards your solicitors costs and they may well deduct a further % of your compensation, they will also deduct 300.00 being a proprerty damage excess.
Good Luck