1. I regret to say that there is no appeal from an offer by an insurance company but you can go to court and litigate about whether the compensation is sufficient within the terms of the insurance policy. There is an Insurance Ombudsman but he only deals with cases related to mis-selling or other situations where there is a legal wrong. Accordingly, you should satisfy yourself with the offer before you accept it. You can go to court and litigate about the amount of money which should be properly payable. However, this will involve time and effort and some expense if you employ a lawyer. So you need to consider whether this is worthwhile where there is only £335 in the difference. That is a judgment call only you can make.