I would allow the other party 48 hours to furnish the details, after that, I would report it to the police. You can find the insurer details by using ownvehicle.askmid.com/ you can then contact the at-fault insurer directly, if the damage is sufficient enough it will require repairing irrespectively. I would still contact your insurer and report it "for informational purposes only" at this point, but advise you "may" wish to claim in the future. It will have repercussions irrespective of what you do, just because you have been involved in an incident and made a claim (even though not your fault and you may have claimed via the other insurer) they will still seek to load your premium.