We have a vertical strip of external damp rubbing down the gable end of our house.

without looking at the issue its impossible to say exactly what is causing your dampness, your best bet is post your job on the site and get a local expert to asses the issue preferably one that is a specialists in older buildings. good luck Alex

hi, i have had two costumers with the same problems, the problem is that the masonry gets saturated and just don`t get enough time to dry out before the next soaking , i suggested to the first costumer that we try a water repel-ant sprayed over the stack, two coats applied , that was at least 10 years ago, work perfectly and was not expensive, done another one since and had same result, also did not take many weeks to dry out. pointing, flashing and benching around chimney pots needs to be in good order , hope this may be an option for you

In my opinion , you have no cavity wall so water could be penetrating the wall and soaking though ?

Sounds like no overhang on gable so water could be backtracking if you had any photos it would be easier to diagnose