It is quite clear that this is how the system works.
The Road Crash Unit for that particular Police Force will hold all the records of the crash.
You inform your insurance company about the crash and furnish them with the relevant Crash Reference Number.
Your insurance company will then contact the Police to obtain details of the other driver and the details recorded by the Police of the other drivers insurance company. They will then contact the other parties insurers and begin the process of recovering costs for your repairs. In the meantime your insurance company will contact you and organise for the repairs to your vehicle to commence.
Simples!
Pretty much.
(Where applicable) The Police fill out long winded report forms for collisions etc which list out the cars, drivers, passengers, insurance details, injuries, road conditions at the time, events and likely contributing factors to the cause of the incident. This is then filed away as already said for the insurance to pull from the Police.
Amongst other things, filling in the form is done on behalf of the insurance company, who would have had to do the same work anyway. But as its cost the Police time and effort to do it, for an action which may not necessarily be a criminal issue ( i.e. Not necessarily a Police matter ), the insurance companies are meant to pay a fee to get the form. This helps pay for the Police's time and effort to do the work. Some companies try and pap the getting of the info onto the drivers by asking them to pester the police for it and so avoid them paying the fee.
I may be worth pursuing a little more though, as there is a duty for the driver to leave more than just a phone number .... as below.
( This is greatly paraphrased by the way, but is the salient points )
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S.170 - RTA 88 - Reportable Road Crash
If crash occurs owing to an MPV ( Mechanically Propelled Vehicle ) on the road, it is reportable if
• Personal injury other than the driver occurs
• Damage caused to other vehicle or trailer
• Injury caused to animal not being carried
• Damage to property ( permanent fixed items, not bins etc ) is caused
S.170(2) - RTA 88 - Stop and Supply Details
Driver of an MPV involved in a reportable crash must
• STOP
• Supply details to any person have reasonable grounds to need them
• Name, address, VRM of vehicle
Offence not to stop and supply details.
S.170(5) - RTA 88 - Produce Insurance
Where a reportable crash
• Involves personal injury
• To someone other than the driver
• The person must produce their insurance certificate at the time of the crash
• To a constable
• To any other person having reasonable grounds to supply need it.
Failing that, report to Police station as soon as reasonably practicable within 24hrs and produce certificate then.
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So OK, he's contacted the Police within the 24hrs, but he could have left you a bit more than just a phone number.
Ultimately, I think the insurance is the route to go and hound them.