It is not the responsibility of the tree owner to prevent their trees from overhanging an adjacent property. If branches do overhang your property then you have the right to cut off the branch without the owner’s permission ensuring the work is done to arboriculture standards and does not harm the tree. The branches can only be cut back as far as the boundary and you have no right to cross the boundary to do this. This could be classed as trespass. Any branches you cut off, as well as any fruit, remain the property of the tree owner. You should not use or dispose of the pruning’s or fruit without the owner’s permission. To do so could amount to theft or even criminal damage. However, it is not advisable to just throw the material back over the fence, you could be prosecuted for fly tipping with penalties of up to £50,000 and/or 12mth imprisonment. It is advisable to ask the owner if they require the branches back but if they do not then it is your responsibility to dispose of them. Roots which cross a boundary can be dealt with in the same way as branches but much more caution is needed. If the tree dies back or falls over as a result then the owner might have a claim.