WRT the police involvement, I have been speaking to a few TDO to put an article together for Westfield World and they are very clear on the Track Day v Experience etc. As they put it TDO that are registered with the Association of Track day Organisers (ATDO) https://www.atdo.co.uk/ will have an RTA waiver/exclusion with the relevant local Police force that in effect turns the Track into a private road and hence not subject to the Highway Code or normal traffic law - hence you can drive an un-MOT'd and Taxed, insured etc vehicle. If the TDO or Circuit doesn't have an RTS exclusion (and there are plenty of them) then any accident is considered an RTI and can be investigated by the Police - however, they did say this is generally only when one or more parties are injured; if you stuff it into the Armco and walk away then most likely nothing will occur.
This is further compounded if as @Blatman said one or more party has insurance and hence wants it to be investigated and recorded officially in order to validate a claim.
The final point being that if the RTA waiver is not in place and the Police do visit (at any point not just post accident) then anything that is illegal on the cars COULD and I do stress tha, be actioned and fines issued. So in the case of the BMW and the Civic they may check to see if the cars were road legal or had Mods that may have affected the outcome?
The TDOs I spoke to suggested always check the registration of any TDO, especially any that are one-off charity events or groups of mates booking a day as they may not have full cover.