As its got a TPO, consult your local council regarding the problem. They may want to inspect, and may insist on a tree surgeon.

your other option if its not to big a limb and you dont want to fall out with your neighbers is to go andexplain this to the nieghber and just trim the burnt stuff of . if its bad then i suggest doing what bamboo sais . its possible it looks worse than ity is and a couple of years growing will hide it . if its not your sideof the fence and not hurting the tree i mite just have a word about future fires etc and leave it x . theres nothing worse than having neighbers you dont get on with .

I think you have to ask the council before you can cut much off it if its got a TPO. And going through the official route should make your neighbours realise they need to be more careful another time!

Thanks have contacted council and awaiting response. Don't want to fall out but do want to be clear that we all have a responsibility towards protecting the tree.