A few nights back I covered my potatoes with some of that hort fleece (its the type that seems to be easily ripped apart) and the wind must have blown the cover and so upon checking my potatoes the next morning frost had hit them.
Most of the leaves are blackish but there are several leaves on each plant that have not been troubled.
Is it the end for the potatoes? What can I do? Should I cut off the damaged leaves?
As long as there is some living tissue and the tuber isn't damaged, it'll probably be just fine. If there is a lot of dead tissue, you may want to cut it off to avoid mold and disease spreading throughout the plant.
Best of luck