If your neighbour's tree overhangs your property, this is a form of trespass. The neighbour should be asked to trim back the tree. If he doesn't, you haave the right to trim the tree back to the boundary line, although any branches and/or fruit removed belong to the tree's owner and should be returned. There is no precedent for recovering the cost of pruning the tree from a neighbour, or transporting the branches back to the owner. Before pruning a neighbour's tree, you should first check whether there is a preservation order on the tree, and, if there is, you need to approach your local authority before taking any action.
If your neighbour's tree is very tall, or blocks out light from your property, you can prune the roots or branches. However, you should not reduce the height of the tree without obtaining advice from a solicitor. If you have to enter the tree owner's property to do this, you must give reasonable notice. You may also wish to consult your own insurers, if there is a possibility that your property may be damaged by the roots. If the roots have already caused damage, the tree owner is liable to pay compensation, but it must be shown that the tree owner knew, or ought to have known, of the danger.
I know you have said that your neighbour is unapproachable, so I would suggest that all communications are in writing - either personally or via your solicitor.