Presumably this arrangement makes for economy of cable.

Yes, although this arrangement is now deprecated as it interferes with
hearing aids and might even have implications under the disability
discrimination act.

Can this type of single core cable still be obtained?

No need. At the existing light locations, drop a 1mm T&E down to the socket
and wire it up as if it is was the existing light fitting. As you will need
to bury these joins under plaster, you should crimp the connections (and
probably solder the crimps for good measure!), heat shrink the connections,
then heat shrink the entire bundle. Then bury in plaster (after testing, of
course).

So should the whole existing lighting circuit be replaced with a loop in
arrangement using twin and earth?

That's an alternative, although a little overboard, especially if hearing
aids aren't used, or you have no 'loop' audio appliances.

Christian.