They cant erect that on the boundary without yr permission but they can have it offset by a few inches onto their side.
They can erect a fence up to 2m high without planning permission.
There is no right to light for gardens.
The only possible action might be in nuisance but to be honest I cant see any grounds.
I am sorry, I appreciate that this isntt he answer that you want but there is no point in me misleading you. I have a duty to advise you truthfully even if that is unfavourable
Does that answer the question? I am happy to answer specific points.
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