The recent pictures seem to have clarified things.
In my opinion, the Constantines built their extension first, observing the boundary-line. This meant that whilst the foundations ran along the length of the boundary the actual wall would be stepped back from this.
When the Alis built their extension, rather than leave a 6" gap (3" on each side of the boundary line) between the two extensions, they butted the external leaf up to the neighbouring extension (including an expansion joint as shown).
This is actually sound practice as the gap can cause all sorts of problems; damp, vermin, litter and by it's very natue it it inaccessible and can be to the detriment of 'both' properties.
There may be NO commensurate appropriation of space internally by the Alis. The Constantines now no longer have an inaccesible 3" x however long the extension is at the boundary of their property, which would have been to the rear of the concrete fence posts.
As more information keeps being added to this newspaper article, I may change my mind later on...