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I don't know if it's the same with unmarked detective cars, but if trafpol are in an incident, nobody can leave the scene until a supervising officer attends the scene. I was involved in an accident caused by trafpol, they ignored us as though their dangerous driving hadn't caused the accident, but luckily my mate who was in the car that got damaged, his step-dad is trafpol. Everyone got a bollocking and someone came round to my mate's house to personally apologise. Police insurance covered everything.
I had a very similar-sounding incident where an unmarked, no-sirens car hit me during a chase. The car was completely at fault. The copper was very apologetic. I did give some details but I don't remember being given any paperwork. Later on he dropped off a £50 Evans voucher. I suspect this was because I didn't lodge a complaint!