Thanks. I'll ask the neighbours to let me go round with a ladder to photo the abutment, measure the coping stone overhang and clean the drip channels. Once I have, I'll post here. It may not be until after Christmas, though. How would we know if the mortar perps and beds are failing. I'm not sure which gutters you mean, or what a membrane and back gutter are. Google wasn't much help either. Which gutter do you mean, and what needs to be done differently? Thanks again.OP,
The verge(s) are not the problem.
A pic of the roof abutment with the wall might show something - its only a possibility but worth a look at how the abutment has been flashed?
FWIW:
the staining on the render below the parapet capping is possibly due to:
1. the coping stones are not wide enough to throw off water and
2. the drip channel under each coping need raking with a flat screwdriver - raking will clear any blockages in the channel.
3. maybe the mortar perps & beds are failing.
The fragile membrane gutter is actually a back gutter & should have been built & lead flashed as such.