(Apologies for long post; trying not to drip feed)
We have a number of big horse chestnuts in our garden, and live in a conservation area. The part of the garden where the chestnuts grow runs alongside our neighbours' house. They are currently having their house extended, and have asked us to cut back 2 of the horse chestnuts as they're worried about conkers falling onto the new part of their property. Apparently a conker has in the past broken a Velux window in their house, though I think before we moved here and I do wonder if it's actually possible (unless squirrels have had something to do with it!). Anyway, they regularly cut back the parts of our trees which overhang their garden, which has resulted in the trees being quite lopsided. I've looked into this and found out that a neighbour has no responsibility to maintain the tree's balance when removing overhanging branches. The branches which do overhang their garden are about 3-4 metres high and are quite small, as they've removed all the larger ones. So there isn't a huge number of overhanging branches, but they still want these removed and they're too high for us to reach.
The tree surgeon has said that, in order to keep the trees balanced, they'll have to do a crown reduction of the whole tree. However, the cost of reducing the crowns is around £850, and I'm wondering whether IWBU to ask the neighbours to contribute, as this is on their request and to their benefit, and there is no real evidence that their property is being put at risk. The trees are otherwise healthy and, as I've said, there are no large branches overhanging their garden.
Wisdom of MN, advise please!