Questions about nuisance trees crop up quite regularly.
Anything which overhangs the boundary, including routes, is nuisance and trespass. The overhanging pieces can be chopped off as can roots growing underground but they do not belong to anyone other than the tree owner, so the pieces should be given back although if they are unceremoniously dumped over their hedge without warning, it is not good for already fraught neighbour relations.
If a complainant is not capable of doing this themselves or do not want to do it themselves, they can charge the neighbour for the cost of doing the work provided they give the neighbour notice that if they don’t trim it, they will get someone in to do it.
If the tree owning neighbours won’t pay up, then it’s a case of taking them to the Small Claims Court for the cost.
Anyone cutting overhanging branches are not allowed to kill the tree or cut the roots back so far that they can destabilise or kill the tree.
I am not aware that it is possible to have a Tree Preservation Order on evergreen trees, although before cutting any deciduous tree always check for Tree Preservation Order.
There have been cases in respect of deciduous trees where the adjoining owner has been made to cut them because the leaves and the loss of light is nuisance. That is nuisance on an ordinary English dictionary definition of the word. However such actions with deciduous trees are not common.
The situation with evergreens, and Leylandi in particular is different. Regarding evergreens, a complaint can be made to the council and they will deal with them under the nuisance tree legislation but only with regard to the height. They want £300 fee to start the process and if they find that the trees are a nuisance, they can compel a tree owner to cut them down to 2 m high.
The following are links will give you some reading with regard to high hedges and nuisance trees. They come from a few particular local authorities but the rules are the same throughout the country. The majority of local authority have pages like this, I just happened to pick these out.
Thank you for letting me assist you with your legal question. I am glad that I was able to help.
I am not certain whether that answers the question for you or not, but I am happy to answer any specific points arising from this.
It will be my pleasure to help you again either further with this or any future questions you have