Suffice it to say that my firm point here is that the view blocking tree is legal “red herring” in terms of justification for its slaughter.
Another important point is that the tree trunk is on your land. So this is your tree. It is your responsibility and by definition should be your decision to take it down. Where the branches overhang your neighbors’ land, they can cut those branches, but must not interfere with any part of the tree on your side.
A caveat against your freedom to do whatever you want with a tree on your property, as well as the right of your neighbors to cut overhanging branches, is that permission is still required to work on a tree subject to tree preservation order, or that is located in a conservation area.
TPOs are a fairly well-known concept, but my clients are often surprised to learn that if they live in a conservation area, all trees are deemed to have TPO. This means that anyone wishing to work on such a tree must apply to their municipality.
You don’t say if you live in a conservation area, but if you don’t, I urge you to contact your local tree manager or, if there is no such person, the local planning department. to see if your tree can have a TPO placed on it. Local authorities will often issue a tree with TPO status if they are concerned that it is in danger. If this can be done without you being involved, it can also ensure that all important cordial relations with your neighbors are also maintained.