Yes, but it happened to me in Putney not Sussex. When I got the tyre replaced the guy doing it casually asked me how it happened so I told him, and he instantly said contact the council and make a claim. So I did, and they were very helpful and sent me an insurance claim form to fill in, 3...
I had the same happen to me recently. Make a claim against WSCC for the damage, they are responsible for the roads and they will have insurance anyway to protect against these issues.