Just a light-hearted anecdote, as it is now (obviously?) the case that police likely would neither attend, nor be interested - although maybe a report is necessary to get an Incident Ref No. (My friend's car - 4WD - was crashed INTO - thyey were on the wrong side of the road and nearly went under his vehicle in their small Citroen; the driver MIGHT have been drinking - but the police didn not come, and although not injured, my friend's vehicle was a write-off due to the location of the damage....)
Any way - my experience - which might show how times have changed in not so many recent years:
A long B (or C?....if there is such a thing) road that I sometimes take is very very straight for most of its' length but then has a few bends that become blind when the verge grasses grow tall/are not trimmed. There are no houses and it passes through some woodland and fields of sheep.
One Sunday morning a few years ago, I was driving down it (literally as has a gentle incline for most of it before levelling out). At that time I had a Passat, so not high enough to see over the tall grasses where the land was more open. I approached the second to last of the bends at a low speed - and encounterd three cyclists spread across the road chatting happily away.
The road was sinply not wide enough for the rules of physics to be broken and all objects occupy the same sapce. I came to a halt as they wobbled INTO EACH OTHER (note this....) and fell over like dominoes - onto the grass verge to their left - which was nicely wide enough for them to not roll down a small slope or hit the fence of the sheep's field.
They were - especially (sadly) the one woman - so pissed at me, just for being there I think...... I did not hit them at all.... No names were exchanged but the woman - with my consent - took a photo of my reg. plate and then screamed at me (NOT with my consent) that she was going to call the Police to inform them. I told her to go ahead, and drove slowly away, somewhat shaken..... I stopped in the next village and called a friend, and we went back to the "scene" and I took measurements and photos; also measured my car and estimated - although I knew roughly, - the dimensions of the three bikes riding as they had, across the whole road - which is at that point barely wide enough for two cars to pass one another, and can only be done with consideration and care.
These three were just pootling along (although fancy road bikes and clothing to match) - CHATTING away, which is the key thing - had they had their wits about them, they would have heard me coming, especially as it was an old-ish DIESEL car, which would give advance warning of it's approach.
So when I got home, I did call the Police, also in "the days" when it felt OK to ring them for advice (and I promise this wasn't the sixties, just a few years ago). I also reported it as an Incident, but was told that, from my version, there was nothing to address by them - as I had suspected would be the case.
I also reported it to my Insurer the next day, which I thought would have no consequences - but it did, ehn it came to renewal I'm sorry to say.
However - later the same week, I was called BY the Police and told that I needed to be inerviewed for "Leaving the scene of an accident". So, they visited me; I showed them my photos and diagrams - AND told them that there was already an indcidemt on record- which they did not know about!!! So, even though the Police did take an interest and follow-up - based on the cyclists making a report - they found the whole thing somehwat laughable whhen they heard what had actually happened, especially as one of the men wanted to claim against me for damage to his cycling leggings - which if I remember, were a particularly fetching shade of purple.....
So anyway - long story short. I do NOT think the Police would take an interest nowadays in the way they did (back!) then, and given what happened with my friend's genuine accident.
In the case of the OP - reversing onto a drive is ALWAYS tricky, although agree it is best to be able to drive off when leaving. But every angle needs to be clear and you actions need to be broadcast as visibly as possible - I would not have relied on ANYone to just realised that I was reversing from the lights....Indicating is also essential I would say. And of course, the patience that seems to be lacking these days.....
I wish you luck with it OP. The hassle of it all is so stressful.
(Interesting to read that reversing into someone is usually deemed fault, as one of my neighbour's friends once did so in an aggressive manner - without indicating, quickly, and in a white car in daylight so the reversing lights were not particularly obvious, nor could I have anticiapted him doing that in that spot - and even then he got out and came at me telling me was going to "f**k me and my car up for driving into the back of him 
Steriod rage I think....)