Paul wrote:

SWMBO has purchased a 4'X3' oak-framed mirror and wants it to hang on
a plaster board wall. It weighs 20Kg.
The mirror has two mounting brackets on the back which I would
describe as a rectangular steel plate screwed to the back of the
mirror with a D-shaped 'buckle' hanging off it (apologies, can't find
it on Screwfix site to get its proper name). Can I put two large
screws with spring toggles, or similar, into the wall and just suspend
the mirror off those?

Have you thought of Velcro?
I used heavy duty Velcro to fix a very large mirror on tiles
above the sink in my bathroom.

Admittedly there is a wide wooden panel sitting on the back of the basin,
but my impression is that the Velcro could safely have taken a large weight.