I thought you were the expert on the letter of the law.
They do have some leeway I think (perhaps unofficially) to decide if an infraction is worth pursuing.
My interactions with the Old Bill (not that there have been many!) have mostly been fairly pleasant - a gentle roadside ticking-off for “undertaking” on the motorway, for example.
One encounter that sticks in my mind was when I had parked my Honda 550 outside a newsagent (in the far off days when I smoked) and came out to find a motorcycle cop in full dayglo regalia paying close attention to my bike’s Yoshimura 4-into-1 aftermarket exhaust system.
I assumed the worst and thought I was about to get nicked for having a vehicle with an illegal modification, but no, he just wanted to know what I thought of it as he was considering getting one for his own bike! (his personal transport, not the police BMW). 
My accident experience has been very rare and ancient, but in the early '70s I think it was, a young man in a mini lost control at high speed on ice and destroyed my Zephyr 6 completely. Fortunately I had seen his plight and driven onto the pavement and come to a stop so neither I or my young family were in the least injured.
Perhaps someone told the police, but certainly I didn’t, and, as the young man concerned was the son of a senior police officer meant that it wasn’t necessary. 
We have been talking about reporting damage to third parties. Both your car and the young man’s car were involved in the accident and there was no need to report it if nobody was injured and you sorted it out between you. If however you had run over a parked bicycle when your car mounted the pavement you had a duty to report that. The owner of the damaged bike would have been the third party.
I made a particular point to avoid that bicycle. But more seriously I had to time to pick my spot because we were near the bottom of a long hill and I saw him in trouble as soon as he came into view over the top. he was slithering from one side to the other and I was trying to estimate which side he would be when he arrived. Unsuccessfully as it turned out.
Incidentally, he was saved from decapitation by not having a seatbelt and the bonnet of the mini sliced through his windscreen at the point when he was thrown forward and it went over his bowed head. 
That changes nothing. 
You have always had to report damage to third party property.
And what happens if you don’t? Nothing in this case, nor in another when I was a very new learner in the '50s sideswiping another car when taking a corner too wide.
But you didn’t do any damage to a third party. That’s the point.
Well, apart from the car I sideswiped by taking the corner too wide you think?
I am not disagreeing, it was me who asked the question because I didn’t know. I was always led to believe that the police were only involved, apart from traffic management of course, if there was injury to a person involved.
If no-one is agreeing with that I must bow to superior knowledge and accept this new, to me, concept. 
I have a UK registered car which I want to change to a French reg one. I have a COC but do I have to pay Import duty via Ants do you know? I know about how long they take to reregister a car, but since Brexit, would I have to pay import duty? Thanks
Just think about it it you hit somebody else’s property like a gate, parked car or bicycle or even a motorway crash barrier or bus stop with your car you are responsible for the damage. That damage needs to be reported. When you hit the Mini both you and the other driver were involved in the accident and there was no damage to any other property so there was nothing to report.
The import fees have to be paid to the Douanes. There should be an office near to you.
Oh I see, so we are not talking about reporting damage to other vehicles then, just innocent possessions of any other kind. I can see the logic of that obviously though I still think that an admission at the time followed by an insurance report would be sufficient. BTW just to be clear, I didn’t hit the mini, I was stationary at the time.
Yes exactly. 
Well bugger me, that certainly wasn’t made clear earlier up the thread which is why I questioned it.
I know you were stationary but you were part of the accident.
About 500m up the hill from my house there is a T junction where people either go straight on to the town or turn right to go elsewhere. It’s a fairly tight right turn especially when approaching uphill. When you turn right you pass between a house on one side and a fence on the other. At the end of the fence there is a short stone wall. Possibly once a year a passing lorry takes out the wall when turning right. The driver should report that damage to either the homeowner or the police as they are responsible for the repairs.
It was made clear, the words third party covered it.
Just at the moment you convince me, there you go giving the lie to everything. Isn’t that what I believed,
So not the law to tell the police then. My head is spinning. 
If you talk to the homeowner they become the second party.
If you are moving to France from the UK with all your worldly goods then there are exemptions.
If you live here already then you will need to pay 10% duty and then 20% TVA (VAT) on top, based on the value of the vehicle. The value would either be from a receipt when purchased if recent or the Douane do have the right to value it.
The Douane will want to see the car when you arrange to go to the nearest office to complete the process. Once you have paid and they have processed it, they will send you a 846a form (known as a quitus fiscale) which will then enable you to start the process of immatriculation on the ANTS system.