Web Master:
Hey Flossie, It could be Freckle or Shot Hole although it is hard to tell.
You could try spraying with Yates Fungus Fighter, but it sounds like some good husbandry is really required for longer term plant health.
Prune the trees, this is paramount, feed them, clean up the area under the trees and provide irrigation.
Make sure you rid the trees of any branches which look diseased and dispose of all the prunings in a sanitary way ie: burn them or bury them deeply away from the orchard.
Given time the apricots should respond well, they don't like to be neglected!
Make sure that no fruit from any of your trees is left to rot on the ground as these may harbour pests and disease.