Handle a Minor Car Accident Correctly

Your hands are shaking, someone is already on their phone, and you cannot remember anything except that you should exchange insurance details. This runs through the exact sequence: safety first, what to photograph, what to say and not say to your insurer, and what to do if the other driver disappears.

I have just been involved in a minor car accident. Walk me through what to do in the correct order, starting from the moment the vehicles stop. Cover:
1. Immediate safety steps (first two minutes)
2. What to exchange with the other driver and what to photograph before anyone moves the vehicles
3. Whether to involve the police and when you are legally required to
4. How to report to your insurer and what to say (and what not to)
5. What to do if the other driver will not give their details or drives away

Assume UK roads and UK law. Keep each step brief and specific enough to act on immediately.