Car insurance pays for damage, tries to claim back off property owner.
If it can be shown that the property owner was negligent – he knew or should reasonably have known that the tree posed a risk – then he or his household insurers will pay out.
Further complicated by strength of wind – if it fell off with a bit of breeze, rather than the a storm, he may have thought to get it checked.
IANAL but I used to be an insurance claims manager.
Parents neighbours are having fun as they have a tree that sheds small branches onto the street, and were worried about such a situation, so wanted the tree crown reducing in size to reduce the risk. The council won’t let them as the tree is protected. The council have failed to grasp that by refusing permission they have potentially taken on the liability should anything happen. (IANAL but my best mate is a H&S advisor for the neighbouring authority)
If you have big/overhanging trees, get them checked every few years by an expert for your own, and your insurers, piece of mind.