Thanks for your question. My name is ***** ***** I will try to help you.
These type of situations can be very frustrating. From the facts stated, you do not have to give your neighbour access particularly if you feel that they already have a possible solution to undertake the works which they want to undertake.
That said, your neighbour can apply to the court to get an order to access your land. The court then may grant access under either the Party Wall Act or the Access to Neighbouring Land Act, depending on whether the boundary feature is a party wall or not. Your neighbour will be able to access your land in circumstances where otherwise that would constitute a nuisance or trespass at common law.
As to your neighbour's conduct. This sounds like harassment, the test for this is subjective. It is if you feel intimidated / threatened. You can report such behaviour to the police.
I hope this is helpful.
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