Unfortunately, your insurance company has a right of subrogation which means that they can act for you in any claim against you that relates to the insurance policy that you have taken out.
Therefore, if they settle in the TP favour, this will obviously count against you in respect of your no claims bonus.
It appears you have given very clear instructions to your insurance company as to a fraud and so if they decide to settle and increase your premiums or reduce your NCB then you have a right to make a complaint to the Financial Ombudsman Service.
Reading the thread further, it does appear that your insurance company are now treating it as a fraud and should go to a fully contested Trial. However given the backlogs in the system this may be some 18 months away.
The letters being posted through your door are likely not to be from the TP insurance company but their solicitors. Your insurer's advice to ignore them is not exactly the right thing to do. You should send them on to your insurance company for them to deal with and write back to the sender to advise them to send all correspondence directly to your insurance company.