Very nice pleb. By chance you photographed a structure that not many people see:- on your 7th photo, there is a brick 'domed' construction down to the left of the wall.
I think it could have been an old ice house, it certainly looks like one.
I've walked on Lord Mayor's Walk towards Jewbury on lots of occasions and only saw that for the first time a couple of weeks ago. Hidden in plain sight, as they say.
I never tire of the views of the Minster and the one you've got looking up at the back of it is a cracker