The esb had someone cut the branches around the wires, but the branches above are left be.
When I asked my home insurance company if we were covered for damage from falling branches and/or trees, they told me I needed to inform our neighbour in writing that we were concerned about the problem and if she did nothing and a tree or branch fell causing damage, they would go after her for compensation. They also said that I should tell her that if she was advised there was a problem and she did not act, her own insurance company may refuse to cover her and that would make her liable in person.
For seven years we lived with neighbors trees and unfort are still living with some.
Before we built we immed discussed "gutting" them at our expense, NO, then trimming "DO NOT TOUCH OUR TREES". Left for three years, no light, dirt of them unbelievable.
We rang esb as we too had power lines at the back of our property. Came out with huge tractors and pizza like saw and what they removed was so disappointing, considering they had the man power and equipment and time as they spent ages standing around, why they didnt gut them I dont know.
Eventually edge of one tree canopy was touching the side of our house. Took advice re the trees, yes u can trim anything hanging over the ditch and throw it back in. We informed the neighbor. We did it and what a difference but still no light and dirt.
Left for two years and then a neighbours tree of similar size and age fell blocking the road. Checked with our insurance company and told the same as you. We approached the neighbour, who said he'd farm insurance and would look into it. Heard nothing.
Then another neighbour happened to be in with him about year later and didnt a huge branch just creak and fall off another tree and nearly got the pair of them. We were immediately told of this and decided to act. This time we got his permission to cut them as we harped on about a real danger to our children (which was a real fear).
We could only afford to cut the crowns off the trees, have huge trunks left which unfort this year have sprouted new foliage. But the result is amazing, our house during the winter is like a heater was shining on it. No dirty leaves, moss, twigs, sticks, even branches sometimes falling into our property. Our gutters needed to be cleaned every week, we'd even put gutter barriers up but still small stuff got in, leaves collected like a carpet on the gutters.
There is still a line of conifers left but we'v left them. Cost around 3K in total to do what we did.
We also contact the local council as some trees were on the roadside of the ditch, heard nothing/nothing done. Also local politician, nothing done (yet I suppose I should add).