They are TREES .. so the tall nuiscance hedges (evergreen or semi-evergreen) cannot be used with your local councile if neighbour will not do anything about it.
The only chance of forcing an issue is if any branches/boughs can be regarded as dangerous (or a risk) to property or underground damage. (For instance, if there were dead branches falling from 20ft from boughs, damage by overhead boughs to your roof, or damage by encroaching roots.
In these above circumstances .. even if tree has a preservation order on it, the work may be done to lop or root prune the tree.
If no order existent, sueing neighbour for remedial work may be a way of forcing them to lop or heavily cut back the(se) tree(s)
If you are in a conservation area, I believe any tree becomes protected (and TPO conditions then apply) as the trunk exceeds 30cm diameter.