?infestation causing plants to turn black

My Dad has an problem in his garden, many of his plants are turning black. He thinks it may be 'soot rot'. It looks like there is a tiny pale coloured insect under the leaves.  He has been using sprays to kill white fly and scale fly but we worry that we may not be able to kill all  them as so many leaves / plants are affected. The black comes off some of the leaves quite easily, others require a good scrub but impossible to clean all of them. Does anyone have any advice?

Many thanks