Andrew Gabriel wrote:

The bulb contacts are riveted into a pair of ceramic holders; here's a
picture https://www.dropbox.com/s/2mscxp11nl3u4d3/IMG_0238.jpg?dl=0.

The wire is crimped into the contacts, in a very inaccessible way. I
think the only way of rewiring onto those contacts will be to drill out
the rivets, then rivet them back in again once I have replaced the wire,
unless anyone has any better suggestions.

They aren't rewirable - the wire is part of the lampholder.
The wire is specially high temperature, and sometimes steal
rather than copper to cope with running continuously at high
temperature, and with very high temperature insulation.

Are those ceramic holders a standard kind of fitting?

Looks like part of an R7s lampholder, but as I can't see the
contacts, I can't be sure.

Thanks, that's exactly what it is.

The arrangement is very similar to some of the ones at
http://www.cordsncables.co.uk/acatalog/R7s_Lamp_holders_for_double_ended_linear_tungsten_ halogen_lamps.html
-
http://www.cordsncables.co.uk/acatalog/EMC%20A02%20R7S%20PG%20106.jpg
in particular.

In that case I will just take care of splicing it properly.

If you are rewiring, I would look to changing it to take a
different type of lamp. I rewired several halogen uplighters
a few years back, to take LED retrofits for 2D fluorescents.

That's a good idea. What sort of LED did you use?

Daniele