I looked at your first pics and I have had identical black spots on my chinese elms. Mine did not look like the
@jeremy_norbury pic. Over time the leaves tend to yellow. They were in a range of mixes from peat to pumice/bark to akadama. I believe it was fungal. Over the years I have treated with mancozeb, daconil and copper at various times throughout the year (the benefit of our arid climate is that it doesn’t wash off!). They all seemed to be effective as a preventative. I also was more careful with overhead watering. Now I usually see it on some scattered leaves around the garden in the late summer or early fall. I remove the few leaves as I see it to avoid having take off too much at once, although elms could take it fine.
I started acidifying my water a couple years ago which took care of some nutrient lock deficiencies and I think that also helped strengthen the trees to fight off fungal attack.