Be very careful about writing anything to them as if it turned out you later needed to instruct solicitors and pursue a case through the courts you may end up having seriously prejudiced matters by trying a DIY version first by what you say, don't say,propose etc...
Chances are they will just refer the matter to their insurers who will pass it to their legal advisors and you would end up having to go up against solciitors in any event which is not advised without having your own representation.
Find a reputable PI firm and ask for a free initial consultation to get their advice as to whether there is a potential claim there, how long it could take, the costs if involved, the potential financial ramifications if you don't succeed, possible compensation etc...