Thanks both. I wasn't in the car, I saw it happen from inside a shop. One of my sons was in the back of the car though. One of the shop employees saw it, as did another of my sons, so I would hope I was fairly well covered in terms of being able to disprove a change of position on the other party's behalf.
My insurance policy says to "give us as quickly as possible, full details of any incident which could lead to a claim". Since I would only claim on the other party's policy (which I'm not going to do), and they won't claim on mine (for the aforementioned reasons), I don't think that what's happened matches the statement in the policy.
The main question as far as I'm concerned is whether or not my insurers will "get wind of" the nudge as the other party has reported it to their insurers, but doesn't have my policy number, although they do have my name and reg.
My wife's car was damaged in a car park when we were away from the vehicle and the "offender" left a note. It sounded like they would have needed to claim on their insurance, but we took no action and just touched up my wife's car ourselves. This seems to be a similar situation, in that they would have had her reg to cite when telling their insurers about the incident, but I don't really see why they would even need it. I appreciate that my insurers would be interested to find out as my vehicle will now be at greater risk in their eyes than previously, and would consequently up my premium. However, as I mentioned earlier when quoting my policy, I'm not sure that this incident requires me to tell them.