We bought our council house a few years ago. The property deeds say that one boundary is our responsibility, without stating exactly where the line of the legal ownership is. There are concrete posts along the boundary, which we are responsible for replacing when the need arises; can it therefore be concluded that the line along the outside of the posts is the boundary?
It sounds as though the boundary line will be as you suggest. So if you wanted to replace the posts with a fence, for example, you could attach the fence panels to the outside of the posts. This is why most homeowners see the “worst” side of their fence, or at least the side with the posts. If they attached the panels to the inside they would lose the benefit of a strip of their garden.