Mystery hedge infestation

Help!  I'm an absolute heathen when it comes to gardening (not actually having a garden), but I am very fond of the small hedge at the front of my Victorian terrace.  Sadly, it is under attack from I don't know what and I'm afraid I'm going to have to remove it and start again.  I've always referred to the hedge as privet, but my wife thinks it's laurel.  All of the leaves, and all of the woody bits, are covered in what look like tiny white insect eggs.  There must be millions of these things.  However, if they are eggs then they have been laid in very random patterns and not in clusters, as I believe is usual.  The "eggs" can be removed from the leaves using just water and some gentle rubbing, leaving the leaves looking glossy and relatively unharmed (to my eyes).  I can't, however, find any adult insects on the hedge at all. It's at the stage now where defoliation is occurring, and I fear the end is nigh.  Any advice would be welcomed.  If I have to start again, do I need to replace the soil?  We have noticed mushrooms growing in it recently and that may or may not be significant.