You could draft something such as :
"Dear (name of driver),
Without Prejudice Save as to Costs
I refer to the incident on 4th August 2018 at (time) on (location). I have taken the opportunity to seek legal advice. Given the interaction between our respective vehicles, I was hoping that you would stop and exchange details, as per the law. I have also spoken with the Police on (date), who suggest that this is a civil liability matter. Liability is not admitted, however, in an effort to reach an amicable conclusion, I propose the following:
1. I will pay for the reasonable cost of the mirror to your vehicle please provide a quote for repairs); and
2. You agree to pay for the cost to mine (quote attached), within 14 days.
3. Upon agreement to 1 and 2 above, the matter is concluded in full and final settlement.
I look forward to hearing from you shortly.
Yours sincerely, "