Patrick Newman, good evening.
First of, I know nothing to speak of about the Party Wall [Stuff] I fortunately live in a country where such niceties simply do not exist
From the image posted? it is odd in that the neighbours Dormer cheek facing on to the property you are concerned about has been clad with what appears to be roofing slate?, some of which have fallen off??
What is of great interest is that the chimney head you are concerned about appears to have been clad in a similar fashion, with roof slate, a lot of which have fallen off exposing a chimney head not in the first flush of youth?
There is a possibility that the chimney head forms an integral part of the neighbours dormer? that being the external wall TO THE DORMER.
What may?? have happened is that during the work on the [formation??] of the dormer, there might have been some sort of "formal" or "informal" agreement that if the neighbour incorporated the chimney into the "new" dormer the neighbour would waterproof / assist in stopping the dampness from an old === at that time=== leaking chimney head, by cladding the entire chimney head with roofing slate, even the side of the chimney head the neighbour was not actually responsible for ??
OK a load of pure conjecture, BUT?? why is the dormer cheek and the chimney head clad, or has been clad with roofing tiles???
As for the "Legal Position?" suggest the conveyancing Solicitor is asked to enquire int the above to see if anything exists??
Ken.