I've successfully had a neighbour take down a new structure by citing my
“Ancient Light” rights which basically meant that I enjoyed the daylight coming through my windows for many years until you built your structure.
Unfortunately, Ancient Light Rights don't appear to cover trees and won't be considered, excepting the matter will be considered if you need to have your electric lights on during the day. As described on this Gateshead Council's website:-
https://www.gateshead.gov.uk/Environment%20and%20Waste/Trees.aspx
There's an online booklet which explains Tree Preservation Orders and outlines the action needed when submitting a request - see pages 14 and 15.
https://www.kirklees.gov.uk/business...with_trees.pdf
.