Will the landlord agree to cut these branches off?
Is it just the timescale that is the problem?
Is there any Tree Preservation Order on the tree?
Is it deciduous or evergreen?
How tall is the tree?
Would you be willing to pay someone else to cut the branches off?
If the tree is a deciduous tree and does not hang over the boundary and trespass onto your property, or it is actually on the property but simply prevents you getting a television signal, I’m sorry to have to say that there is nothing you can do about it.
If it’s in a neighbouring property you can cut overhanging branches off and return them to the neighbour and seek the cost of it from the neighbour.
You cannot cut random branches off to get a television signal.
If the tree is in your garden and belongs to your landlord and he simply doesn’t want to do anything about it, that you can’t do anything about it unless he promised, before you went into the property, that he would do this in order for you to get a television signal.
You have a remedy with regard to the tree if it is generally a nuisance but not because you can’t get a television signal. There is already caselaw on this which you will read from this link.
I’m sorry I wish I could give you a better answer. Can I clarify anything for you?
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I really wish I could give you a better answer but as you see, there is case law and hence, you are at the mercy of the landlord. If he will let you cut the tree down that would be fantastic although I appreciate that it’s a cost that you may not want or even be able to pay.