As this is a new cable run and is just being used for earth, could I use
a single core cable (sheathed with green/yellow), or would you advise
using one of the cables from a twin core to get the benefit of the extra
cable protection? I don't want to bodge this, the house has had enough
bodges on it so far by previous owners without me adding to them. I
think the cable run will be easy enough - a channel down by the door
frame and then it can be tucked under the skirting round to the socket.

Running an extra cable off to some other circuit to pick up an earth is
itself a bit of a bodge (not a terrible one, but definitely not best
practice); the "fully right" thing to do is to rewire your downstairs
lighting circuit with new cable which includes the earth conductor.
You'll be able to reuse most or all of the existing cable route, but if
the old stuff is plastered in you'll get plenty of practice in applying
one-coat patching plaster!

Unearthed lighting circuits wnet out-of-regs at least 30 years ago,
which suggests your downstairs circuit cable is coming to the end of
its useful. It's not that likely to be the original 30s you mentioned
in a previous post - back then it would've been rubber-sheathed, and
you'd find that the insulation would be crumbling off it the moment
you unscrewed the old fittings and moved the cable around a bit. (If
that *is* happening, BTW, you need to rewire *urgently*, as the risk
of sparks and in the worst case fire is well above neglible...)

HTH - Stefek