Neighbour Fence Woes

It has been quite a while or at least it feels like forever that we have been planning our new home. We choose this, that, sign here and there, and get various approvals for our home to be built. Well it seems that there was one approval that was not requested. We planned to build on the boundary with our boundary taking the place of the existing fence. Although we have built before last time was in a developing estate with no fences. This time there was an existing fence to complete any works on that fence requires a fencing notice to be issued by us to our neighbor.
During all of this planning and preparation Porter Davis didn't bring this to our attention. The neighbor says that they emailed Porter Davis several months ago bringing this to their attention but nothing was ever brought up with me and they got no reply. The result of it is that our neighbor is refusing to allow the removal of the fence in accordance with the fencing act, for our garage wall to take its place even if only temporarily and reinstalled after. What can you do? I can understand they are bothered that nothing was done about it earlier and having construction next door would be a bit off putting but it is the reality of having neighbors. And particularly when the block lay empty for 10+ years - eventually something is likely to be built there and that is just how it works. Anyway, I don't really want to enter a new street and have the neighbors offside so we have arrange Porter Davis to take 10cm off the width of our garage therefore allowing the fence to stay where it is. For 10cm hopefully we end up without upsetting the neighbors too much.

Update 4/2/2017: Sorry Neighbors your fence blew over!

During strong winds over the weekend the fence in question was blown down. It has been damaged with several panels and posts requiring replacement. Not sure if that was what they were after. :-(