This is a much forgotten (or avoided?) solution to a common problem. The situation arises when there are attached properties (semi-detached or terraced) and both are likely to want rear extensions at "some point", just not at the same time.
Mostly what happens is the first 'side' builds their wall wholly on their land (with Section 6 Notice and Section 1 Notice as necessary) and they have a independent extension. The second 'side' come along at some point in the future and build their wall wholly on their land, often with some difficulty because the first extension is already there. There are then two side-by-side, but independent extensions, with an awkward gap between the two. Both sides have 'lost' a little bit of width to their extension and both side have each had the cost of building a wall each.
What is able to happen, by using the Party Wall etc Act 1996 and planning ahead, is the first 'side' could use Section 1 to have an agreement to build the wall astride the boundary. It is built as an outside wall and their cost initially. Then at the later time, when the second 'side' are ready they build their extension using the wall astride the boundary as a Party Wall. They have Section 2/3 Notices to serve and under Section 11 they pay the Building Owner for the benefit of now not having to build that wall. The cost is worked-out based on the proportional use of the wall, so in the simplest cases of an equally shared wall then it might be 50/50. The cost is worked out on the cost at the time that the second 'side' makes the use, not what the first 'side' paid.
The benefits?
Each owner only has the cost of half the cost of one wall
Each owner gains a little more width for the extensions, by saving the thickness of the extra wall and the gap that is lost between two walls.
So our advice... think ahead when planning rear extensions, open-minded neighbours could benefit.
Also the arrangements 'carry-forward' to future owners (make sure you keep and pass-on Awards, they could be useful!). So even if the initial owners of the properties sell (one side or both) before the second extension is built, then the subsequent owners still get to share the wall and balance the cost between them.