Just to clarify – unless there is injury there is no need to supply insurance details after an accident.
Also if the driver stopped and supplied her details and the vehicle and owner details there is no need to report the accident to the police. For non injury accidents …
“The driver of the mechanically propelled vehicle must stop and, if required to do so by any person having reasonable grounds for so requiring, give his name and address and also the name and address of the owner and the identification marks of the vehicle.”
So name and address of driver and owner and reg number of vehicle are the legal requirements.
http://www.legislation.gov.uk/ukpga/1988/52/section/170