Dying Privet Hedge

I have a privet hedge running the length of my back garden, which is dying in clumps.  The affected areas can be pulled out of the ground quite easily and appear to have rotted (although dry) below ground level.  Websites suggest honey fungus or die back.  I've seen no sign of anything resembling black bootlaces below the ground, which should indicate honey fungus.  The stems of the affected plants have grey/black blotches on them and the leaves are yellow and mottled (I'm new to this or I'd attach a photograph).  Does this ring a bell with anyone?  What can I do to stop the spread? I've filled the main gap (4-5') with conifer plants - was this a good idea, or are they likely to go the same way?