If it has a Tree Preservation Order on it, then what you can do to it or what they can do to it is very limited unless you have consent of the local authority.
There is no right to light in respect of a garden, only in respect of rooms.
You may have a claim in common law nuisance but you don’t have a claim in respect of loss of light
Can I clarify anything for you?
The local authority will have to look at it because generally, there are only two reasons which they will allow a tree with an order to be cut down and they are, that it’s dangerous or it is a nuisance.
You lose nothing by asking.
Whether the neighbours want to cut it down or not is another thing altogether of course.