Two neighbours recently had the exact same leak behind their shared chimney stack.
Some old buildings are beautifully ornate but difficult to weather. An old fashioned way to weather these tight junctions is to use mortar.
Sand and cement is cheap, quick and easy to shape. It will work for a period of time but regardless of how strong the mix is, the second it’s laid you are starting the stop watch on when it will become porus – when it does eventually fail, the ingress can be immediate and quite severe.
Lead work has been introduced to all vulnerable surfaces and once oiled is still very much in keeping with the the aesthetics of the building.
