Sounds like scale insect - google for images, though there are different kinds of scale. Provado make a spray treatment for these, but it affects bees - if you can easily access the worst areas, better to use methylated spirits on a piece of soft material - rub the meths over the scale.

There are various scale insects which look a bit like shells, eg. Mussel Scale. They cover themselves with a wax like substance which makes them waterproof so no insecticide spray can get at them easily. They suck the sap from plants and can do a lot of damage. Fortunately they are fairly sedentary except when very young so do not spread too quickly.
Now getting rid is more of a problem. If there are only a few then a dab of Methylated spirits on the insect will remove the wax covering and it then dies of dehydration. A lot and you are into spraying with a Horticultural soft soap preparation. There is one on the market called Winter Wash. You might need to spray a few times and used a soft brush dipped in the stuff to remove the most obstinate ones.
I have seen a pressure sprayer used to good effect but that would do the flowers on your cornus no good at all.

Snap. except that I have never found the Provado stuff to be good on Oyster scale myself.

I don't use it at all on anything, Owdboggy, as a point of principle - I've already noticed a significant reduction in the number of bees buzzing around the comfrey downstairs - used to be thick with them, now it's just the odd one or two.

Me neither, except in extreme cases in the Alpine house where bees do not normally go in any case. The Hort Soap does not affect bees by the way.