You may have an infestation of minute scale insects which are secreting honeydew, which in turn is attracting the sooty mould. It is a problem I get on my citrus; the answer is to spray for the scale insects. I use something called Conqueror Oil which is petroleum-based - three applications at 14-day intervals. Alternatively, what about oleander aphids (little orange things which look more like pollen than aphids)? They could be attracting something which is producing the honey-dew, and therefore causing the mould.
Let us know how you get on - unfortunately the sooty mould takes a while to wash off under winter rains.