My comment earlier was just pointing out that UK laws on cats are different to those for dogs. They have a right to roam. If you leave your front door open and you get burgled, your insurance might not pay out. If you leave your cat flap open, you may not legally be able to claim for damages caused by a cat. That's if the cat even got in that way. If the builders accidentally locked the cat in, then arguably they could be held liable.
I'm not suggesting that there isn't amoral obligation to contribute to damage costs. But I don't think there's a legal one. It's a grey area. If the neighbours are reasonable they won't take the piss. If they start asking for full re-carpeting costs of the entire house then I think it's important the OP knows where she stands legally.
OK, fair enough - apologies for my misunderstanding.
But either way, I don't see how cats can legally be considered both free-roaming, uncontrollable wild creatures when it suits, but also precious loved pets that the police/fire brigade/RSPCA are allowed/urged to break into people's private property to free them.
Fair's fair: how can it be just for a home owner to be liable for all damage that a cat might do to their house, but also liable to have their property broken into so as to rescue that same cat?