My car was hit from behind while I was driving. Unfortunately, the cars became attached on my tow bar so I had to call my insurance company to get someone out to detach the cars which were both driveable. Now the other party's insurance company wants to take over the claim. Their party has admitted full liability. Their letter states that dealing with them only will not affect my premiums next year or my no claims discount. I am unhappy with the pace of repairs to my car through my insurance company but I am not sure if it would cause me problems to go through the other parties insurance company.