John Stumbles wrote:
Chasing out the wall below the window cill in my kitchen (c. 1970s
extension) I dislodged the top layer which turned out to be about 3/4" of
plaster sitting on slates sitting on the bricks of the inner course, so
that the slates and plaster covered over the cavity. Here's a picture,
showing the cavity now revealed and a little bit of slate and plaster
still crossing it: http://82.21.72.246/~john/cavity.jpg

I'm thinking along the lines of stuffing a few inches of rockwool into the
cavity, fixing a tanalised batten to the outside wall below the windowcill
and putting some artificial slate back across the gap and mortaring it all
up.

I should cut a slot in the mortar under the window, and replace the
slate that you've removed. Not a whole lot of point in pushing rockwool
down the cavity, and I'd use real slate for the job, as artificial isn't
absolutely rigid. Muck up after to replace what you've dislodged.