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 a bit surprised that there was nothing supporting the outside of the
slate + plaster cap so that it was only held by the adhesion of the mortar
to the underside of the slate. I think a bit of levering down on the
outside of it could have broken it away. I don't know if this was ever
legit building practice.

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.

Does this seem reasonable?