Q.Black “fungus”
My large holly bush is covered with a black covering on all the leaves. Is this a “fungus” and is there a possibility of eliminating it, or must the bush be cut down?

This could be Sooty Mold, it is caused by pests on the plants.
https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm
Neem Oil can be used to treat the pests.
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
Please review the links below, as Holly can suffer other diseases that you can access the plants symptoms with.
https://www.gardeningknowhow.com/ornamental/shrubs/holly/diseases-of-holly-bushes-pests-and-diseases-damaging-holly-bushes.htm
https://www.gardeningknowhow.com/ornamental/shrubs/holly/holly-problems-holly-leaf-spot-or-holly-tar-spot.htm