The decision was taken to lift the caps and see what the state of the wall was underneath.
I knew it wasn't going to be good, but I didn't expect what we found. This is supposed to be solid, waterproof...
The "mortar" was cleared off down to the solid surface.
The gaps between caps have been sealed with cement.
On the front face, the base of the stack has been re-rendered and the flashing bound into the wall. Luckily the bricks are still strong and there was no need to replace them.