It wasn't my fault, honest!
With the best intentions, almost everyone who has a motor accident thinks they are not to blame. Believe it or not, even those who plough into the back of an unsuspecting stopping vehicle claim that the driver "was a little too heavy on the brakes".
The problem here can be the setting of unrealistic outcomes for the settlement of the insurance claim. Many clients, having been involved in an accident have having a damaged, but drivable car, don't want to involve their own insurers but pursue the supposed other "guilty" party. If liability is accepted and cut and dried, this is fine. However, this is rarely the case and my strong recommendation is always to utilise your own insurance to get your vehicle repaired as soon as possible and then let your claims manager (all my clients get to use the services of a claims management company, expert in the recovery of losses) recover any uninsured losses on your behalf. Otherwise, what tends to happen is that matters drag on for weeks and months whilst both sides argue about liability. Meanwhile the vehicle remains unrepaired.
This can seem counter-intuitive for clients but is the best approach in my experience.
Key to the matter is early and ongoing communication with all parties to ensure that the claim is heading on the right track.