I think that the right/left side, like the posh side is a convention/rule of thumb thing rather than having any basis in law to be honest Shack.
Because this fence looks really shabby from my side and due to the fact that the neighbours are elderly, I have offered to rebuild the whole thing so that it outlasts us both and we won't have a dispute. I have a heap of new feather edge fencing boards which I acquired recently which I think will do most of it and I'll be able to clad both sides so it looks great for us both. I asked them if they would make a small contribution for whatever extra materials I need. They thought this was a good idea and agreed.
Since then their bloody daughter has stuck her oar in and has convinced her parents that I'm trying to get them to pay for the whole thing and that it's my fence and they shouldn't get involved.
The poor old girl has got quite upset about it, but I've managed to placate her and she seems reassured at the moment.
I guess that's until the daughter gets involved again, but I'll do it anyway and if they don't contribute, I'll just clad my side.