The right to light only applies to light coming into rooms of buildings, not the garden. Even then, it must be reduced by 50% to be actionable.
If these are evergreen the nuisance tree legislation would help you although it’s actually enforced by the local authority so it’s unlikely that they would enforce legislation against themselves.
You are entitled to cut off any overhanging branches and if it means, because of the hike, that you have to get professional contractors into do that, you can do that and then seek the cost is from the council. If you do that, you have to warm them that they are potentially going to incur costs. You cannot keep any branches which have been cut off because they do not belong to you. You must give them back to the council.
You need to check whether there is a tree preservation order on the trees if they are deciduous or of some other interest because you then can’t cut anything without a licence.
What you can do doesn’t bear fruit, make a formal complaint to the Local Government Ombudsman who can look at this decide whether the council are acting reasonably or not
Can I clarify anything for you?
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You are referring to the Trees and the High Hedges Act 2005.
It doesn’t automatically make them illegal. It can make the owner down to 2 m if they are a nuisance. Ironically, it is generally enforceable by the local authority!
Any complaint against the local authority, should be dealt with by a different department and you are still not happy with the result, you can then refer the matter to the Planning Inspectorate and also refer the matter to the Department of Local Government & the Environment, as well as, complaining to the Ombudsman.
It only applies if the trees are mostly evergreen, not deciduous.
I don’t know what was in the mind of the draughtsmen when they drafted the legislation but the main nuisance which it was seeking to address were Leylandi trees.
I am glad to have been of assistance. Best wishes.