This sounds similar to the situation I referred to in my last post. If the other person's insurance is not looking to claim against your son's insurer yet the driver disputes liability you are left high and dry with only TPFT and limited means to make a claim against the other driver unless the insurance company does the right thing. If they have sent over an assessor that is a promising start. Let us know what White Dalton have to say on the subject.
My point was that Direct Line insurance told my mate there was no need to contact his insurance company, presumably then no legal requirement. Steve
Your own insurer is not your friend; they are your enemy just as much as the other guy's insurer. Both insurance companies will be looking to pay out as little as possible now, and gain as much as possible in increased premiums later. If your (your son's) insurer thinks their interests are best served by stabbing you in the back, that is what they'll do. If you are claiming against the other guy's insurance, make up your mind pretty sharpish what exactly you are claiming for in £££, on what basis, and supported by what evidence and arguments. Make the claim detailed and explicit. Make it clear you expect the other guy (or his insurer) to pay 100% of your damage, and you intend to pay 0% of his damage. Once you have done that, you've got to the starting line. Then see if they want to negotiate or fight it out.
You will find that the small print of your insurance policy obliges you to notify the insurer of any accidents, incidents, damages, or claims of any kind, including where there is no claim against this policy. If you don't notify them and they find out later about your failure to notify them, they may be entitled to refuse cover, or charge extra premiums, etc. Being told something on the phone does not get you very far: what is written in the policy document?