I think I would do the same as didyw suggests, its the easiest solution even if you have to lose a few inches of garden. You might need to dig a hole first to see how deep the foundations for the wall are.
If it was me I'd put in some new posts to the height of the old fence alongside the wooden/concrete posts, put down gravel in the gap and then put up your lovely horizontal fencing on the new posts.
Thanks for your input didyw. To clarify, would you leave the old fence in place to preserve the neighbours current boundary being aligned directly above the wall? And then mount new horizontal fence in front of the posts? Or remove the original resulting in the neighbour seeing the posts from their side? I'm happy with losing some garden space to see neat fencing. Thanks all for feedback to date- appreciate it.
Posts