Can anyone explain how to wire up this 2-way switching?
The existing setup: A lounge with one ceiling light controlled by one
wall switch. Cables are twin & earth.

I might be barking up the wrong tree here, so wait to see if there are
any more elegant answers :-}

How many T&Es are in the existing switch ? (unless there are two, I
think this might be a non-starter - and even then...)

Basically you're looking to try to get this:

switch1 ___/--------------------\____ switch2
live from lamp \--------------------/ switch to lamp
*
....but you need a spare core to the first switch to act as the
"strap" to the second switch as you're wiring from the centre* not end
to end.

Then, if you can get a three-core&earth to the second switch from the
ceiling rose, two cores are the strap wires, the third being the
switched live - you can hopefully get creative with a connector strip
:-}

I wonder if anyone makes a more elegant solution in that the second
switch doesn't need wiring at all - it'd be a battery powered RF
device that signals the other to switch electronically...