1. What did the working drawings indicate prior to any work starting? Was this detail on the plans or passed by BCO, & used by the builders?
2. Did the Planning or Regs scrutineers pass plans that involved working, & discharging rainwater, on your neighbours property?
3. How is your tile hung wall finished below the parapet cover flashing? ie. between the lower dormer wall and the parapet?
4. Inserting ply is not the answer - the lead overlaps should be 150mm min. (yours are approx 75mm) so its possible wind & capillary action will allow moisture in.
How far up behind the tile does the lead cover flashing reach? And how is it fixed?
5. Was re-pointing the neighbour's side of the parapet wall, and dealing with their roof flashing, part of the agreement? The original re-pointing is simply a smear-on strip, and the re-built detail is badly done.
6. Why was that section of brickwork rebuilt in place of the demolished chimney stack?
7. Pics from different angles of the parapet and dormer might help.
if I had detailed this I think I would have removed the copings and slapped a big overhanging fillet of mortar in place of the coping to create an even run to have fully supported the lead, then dressed the lead down more. That approach could still be taken with the gap where the chimney was. I don't like the idea of a bit of plywood, it will not sit on the coping well, it's all over the place and I wouldn't wanna be fixing into those copings. As for the state of the wall that's just crappy workmanship and can only be rectified by redoing it.
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