Actually - none of the downstairs light switches have a cable for earth
(upstairs do). I guess I'm going to have to run a cable from the
switch/faceplate to a suitable earthing point - for instance central
heating copper pipe?

NO NO, NOT A SUITABLE POINT. You need to take it to a earth point in a
socket, junction box etc, but do make sure that the connection is part of
the earth circuit.

Dave

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