In all my years of driving, those crashing into me have not done so close to renewal time on my insurance. However, I believe that it is normal practice, where there is an outstanding claim (unsettled as to who is a fault), that both parties loose their no claims, until blame is apportioned.
Once the other persons insurance pays out, your no claims will be restored and you will get back any increased premium paid (due to not having correct years no claims).
Therefore it will gain you nothing shopping around for alternative insurance, since all will consider that you have a claim pending. Of course, you could shop around for insurance, based on having full no claims. Providing that everything is settled in your favour, you will get back the increased premium paid (whether paid to your current insurer or a new insurer).
From the above, it should be apparent to all why insurance companies love �knock for knock� claims � since both parties loose their no claims and the insurance industry wins.
In answer to your question (which insurance company will pay for the repair) - it will be your current insurer (assuming that you are fully comp). Hopefully, in reality, it will be the insurance company of the person who was at fault.