I grew up in a house which had a mature (100+ year old) yew hedge along two sides of the garden - the house had been built in what was originally the kitchen garden area of a big posh house - and the hedge had been planted to make a pretty screen to mask the productive area.
The big house had by then become offices.
We were mortified one year when contractors arrived and cut back the big house's side to the bare stems, where previously the hedge had stretched probably 10' out from stem to tip on each side. The our neighbour did the same thing to "his" stretch of the hedge, and the result looked like telegraph poles. Everyone thought the hedge was ruined, and would never recover, if indeed it even survived.
However, a few years later the cut lengths of hedge had regrown from the (closely-planted) stems and the cut sections looked absolutely stunning, far better than the uncut lengths. Eventually we cut our section, and now, probably 40 years afterwards, the hedge is an absolute picture (my mum still lives in the house).
(Perhaps more extraordinary to the modern H&S fanatic, I and my sister grew up as infants in a garden filled with yew trees without poisoning ourselves or suffering any ill-effects).
The point I am getting at is that in my experience yew, given time, regenerates incredibly well. Although cutting that hedge in the article back to the property line will cause it for a few years to look butchered, it will recover and will look stunning.
It can't be denied that allowing it to grow so far over the wall was a big error of judgement on the owner's part (or more likely a previous owner) and it should have been kept cut further back. The reasons given (actionable nuisance for H&S reasons) are laughable - it isn't a risk - but, to be fair to the LA, some prodnose serial complainer has kicked off about it and the LA cannot do nothing now. (Failure to react properly can be discovered by the complainer by a FOI Act request, and you can bet that they'll persue the LA if there's the slightest hint of improper behaviour). Fact, the hedge encroaches over the wall, fact, the hedge is legally an actionable nuisance, fact, whether or not it is a nice or historic hedge doesn't make it OK. Sad but true. I bet also that the person who complained is a "towny" who's just moved into the village.
It is a stunning hedge and it probably will get cut. It will recover and look stunning again, and to be honest I can't really get too worked up about it. I'd rather it didn't get cut, but we live in a world which is overrun with idiots and imbeciles who have no appreciate on real worth and what really matters, and have absolutely no common sense.
I wouldn't mind betting also that the owner suffers from gout or some such which makes wearing a shoe intolerably painful. Perhaps criticising his slipper amount so making fun of the handicapped and is in rather poor taste!