If your neighbour’s trees are imposing on your garden, you have no legal right to force them to reduce the height or size of the trees. However, if parts of the tree are growing over the boundary to your property then you are allowed to have those parts pruned back (if the trees are protected then permission must be sought from the local planning authority first).
If the tree is protected and poses a risk to you or your property, then we are able to apply to the council under an exemption for dead or dangerous tree works and therefore not have to wait for consent to be granted.