That is not happening to me, but this morning I saw an old Honda Civic (96 reg I think the shape and condition of the same) face an Audi TT, 2006, when she was waiting on fire and the light was red. So he only Audi driver and fled down a side street honking on the left side and put his foot on the floor from the black smoke as he fled. So if this happens to you, how do u claim? Suppose you have the reg number of the other cars.
Start by calling the police. As you say, if you can, hunt down the suspects. Be careful, if they see you in the pursuit, and you think they may try to harm you, you may just want the cops around to make them. Try to stay close to them (but harms way, if you see it) and keep the cops told where you stand.
I’ve been in this situation. A lady in an SUV slid aside in my car when we were heading in a crossing. As I waited on the other side of the intersection, she turned into the intersection. I turned around and saw my car in a parking lot. I was on the phone with the cops now. I box in his car with my car and I waited for the police to talk to him.
I was pretty pumped with adrenaline during the game somewhat, but at the same time, if I could try, felt a gun or a weapon on me, I would have certainly moved away. My life (and every other person in a similar situation) is more than what it costs to repair my car. Also note, there was very little traffic on the roads at this time. If this is the rush hour, and it was not possible to hunt, I would probably just to give the police a description of the vehicle and let them know where she was headed. In the end I was lucky, she had no license no insurance and I had the uninsured motorist in my policy.