Hello and thanks for using Just Answer.
My name is ***** ***** am happy to assist you with your enquiry.
Provided the tree does not have a Tree Preservation Order on it, you are indeed entitled to lop off any branches which overhang yor boundary, provided you return the cut off branches to your neighbour. It is best to hand these back, if your neighbour is amicable. If not, returning them by putting them back over the fence is acceptable.
I hope this assists you and answers your question.
Can I compel my neighbour to have said tree cut down on safety/insurance grounds?
Thanks for the positive feedback.
I am afraid there is no positive obligation on your neighbour to tend to any overhanging branches, and hence you ar eunable to force him to take action if he is not willing to do so.
Thank you very much.