THE LAW. There is a right to natural drainage. This means that water flowing naturally across the surface is permitted to flow downhill into your garden and from your garden to neighbours lower down.
The neighbour or yourself should not increase or channel the flow of water in such a way as to redirect or increase the natural flow or cause damage to yours or your neighbour's land.
The obvious solution is to install a French drainage system described here to dry out the entire garden and channel the water into the drainage system.
However, there are two other things you can do to stop water from neighbours running into your garden.
I have described both ways below.
1. Blocking the water runoff from your neighbours garden is not neighbour friendly as it will cause the water to back-up into your neighbours garden.
Neighbour friendly or not it is a solution I have used.
Building a water runoff blocking wall.
Start by digging a trench as close to the boundary as you can running the length of the boundary to the discharge point. Preferably not back into your garden, but into a drain or the troublesome neighbours garden. Line the bottom of the trench with concrete, leave it to firm-up (follow instructions on the bag) and set the blocks. Ensuring about one third of the block is above ground level to form a channel. Fix the waterproofing membrane on the neighbours side of the wall according to the instructions on the roll.
Back fill the trench on your side.
Building the catch and drain trench.
Dig a trench along the length of the boundary with the neighbouring garden towards the place the water will drain too. This type of gravel drain need only be about 6" wide and 12" deep.
Before filling with gravel, line the trench with landscape fabric to keep earth out of the gravel and allow water to percolate through easily.
Fill the trench with 20 ml coarse gravel . Wrap the fabric
over the top of the gravel and hold the overwrap in place with gravel or a few larger stones, For more detail about constructing French drains visit my garden drainage page.
There's better way to deal with rainwater runoff