What would happen if you call the police if during a lane change your car was hit at the rear by another car and both drivers are not sure who is correct and are at doubt?
The police are better at determining the fault, they can gather all the information from both drivers and witnesses. It is always better to call the police. If you and the other driver swear it wasn't your fault to the insurance company, it leaves a battle and big mess ahead. Technically, the person who rear ended is the person At Fault unless you cut him off and there are witnesses to prove that.
In the UK it is common place that there is a dispute as to exactly what happened in a RTA. You are correct to inform the police - the police should attend at the scene and take details and photos and make notes as to points of impact on the vehicles involved. This information can determine exactly what happened and who was at fault. Please see the related link explaining how to show how a RTA happened using a motorcycle accident as an example.
