if it is in there property it is theres they can pretty much do what they want with it,unless thre is a clause in the deeds saying its yours etc, in 20+years in the building game i have never heard of your stack being in another property, its more like they have took too much out as the stacks run back to back
but on another note any structural works need to submitted to building control with an application saying what they intend to do,had they had done this a bc officer will call throughout the works to make sure its all done above board , i suspect they have not, you should contact your local building control office and let them know whats happened, they will send someone out to sort it out and more than likely back you 100% if it goes to court
what appears to have happened is that the midfeathers or the bricks between the flues have fell into your side making the mess etc it does happen alot as these are old and loose at the best of times, i took my stacks out my old house but i knew what i was doing ,there builder doesnt and is now in a pickle