From my experience, when the accident is not your fault and the other party has admited liability, you have the option of dealing with it directly, or through one of these contingency practitioners (No Win NO Fee) which means you have no requirement to contact your insurance. However, you will note from the small print of your insurance contract, you are required to give them notice of any accident.
In addition, you will find that they will be able to argue your case for you far quicker. Thiis happened to me and my insurance waived my excess ree and got the car fixed and claimed the money back (Did not effect my no claims bonus at all)
Good luck.