What was your relationship like with the neighbour before the letter started. I am assuming you were not on good speaking terms as he/she may have approached you differently if comfortable in your company. I find that nasty letters are a sign that this person does not want confrontation yet will happily threaten and put his/her feelings forward in writing. Thats perfectly fine and therefore your response, through solicitor or otherwise, should take the written form.
If the trees do not pose a safety risk to persons or property then it isnt a matter that the police can or will take seriously I am afraid, it will be noted as a neighbourly dispute and left in a file somewhere!
However, you need to be clear on your position. Are you willing to remove the trees? If the trees were in situ before the neighbour or indeed yourself moved in, would you ask for the cost to be shared as it is them making the demand of you? Are you feeling threatened or uncomfortable as a result of the letters? Do you forsee any other resolution other than cutting them down or flat out ignoring the demands? Once you are clear on your position, and if you can affors it, yes, get a solicitor to represent your view and write to the neighbour, that would be phase 1.
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