In the case of the uninsured car, yes you could sue, but whether it would be worthwhile would depend on whether the driver had enough in the way of assets to pay up. In the case of the car port you can only sue successfully if the tree owner was negligent. Say for example they had been told by a tree surgeon that the branch was diseased and liable to fall and had done nothing about it. If it was just a case, however, of a very strong, unexpected storm (think hurricanes and Michael Fish) then you have no one to claim against. You would have the same problem if it was a lightning strike or broken windows due to hailstones. to paraphrase the advert - where there's no blame, there's no claim.