How do I stop next doors ivy plant encroaching into my garden over the fence?

Reiterating what William Bradley said, there's not really a lot you can do about it but keep cutting it back. If, however, it starts to damage walls (as Ivy can often do) then I would suggest getting the Council involved. The problem with Ivy is that the only way to stop it is by destroying the root with a specific root killer. The problem you obviously have though is that the root is on your neighbour's side. Sorry couldn't be of more help. You could, however, try talking to your neighbour about it.

I agree with the comments already placed you need to find some common ground with your neighbours and come to some kind of agreement possibly the neighbour could control it a bit more from his or her side!!!!!! Regards Ken

you cant stop it. but your allowed to cut ne that grows into ur garden as long as what u cut off u give bk. if it damaging walls or fences that belong to u id check with the council first to see where u stand rights wise then if u have a gd relationship with next door talk about what can be done