A good idea is to have a trusted contractor present to give a second opinion. Just make sure that an argument does not break out between them. It could cost you a decent claim. This one is vital. Keep good notes on all contacts you make with the insurance company and the assessor.
Insurance companies are notoriously bad administrators.
It is not unheard of to find that they have lost your entire file. Keep copies of all written correspondence and claim forms, cocument names, dates, times and who said what. Don't agree to a final claim settlement until you are satisfied that it is fair. You're entitled to obtain independent estimates if you wish. Get more than one quote for repairs.