It is a pretty easy operation and the steps were carried out as follows:
Remove the lamp cover and light bulb.
At the base there is a tapered key that hold the wires in place. Push it down and remove it.
Unclip the lamp from the top of the mast and pull the wires out of the mast
The brown wire is soldered onto the brass tube through which the yellow wires runs.
Unsolder the yellow wire from the bulb base contact and cut it off
Cut the brown wire off as short as possible.
Remove the brass contacts for the old light bulb. Just pull them off.
Solder some coil wire to the shortened leads of a 3mm white LED
Mark the other end of the wire that is soldered to the cathode side of the LED. The cathode side of the LED has a flat side. I marked the wire by scraping the insulation off the other end. Twist the wires together and thread them through the lamp housing.
Place some insulation inside the metal lamp housing and check for fit.
Tie a knot in the end of the wire that is connected to the cathode, and strip the insulation of the other wire. The knot is now the cathode marker.
Paint the LED with orange acrylic to give the lamp a phosphor lamp look (or whatever color you want).
(white spot is a figment of the photography)
Solder a suitable resistor to the cathode side. (It could be either side but my convention is to use the cathode side as an additional negative marker .)
Thread the two wires down through the lattice. Clip the lamp back onto the top.
I did not reuse the tapered base - I just looped the wire around one rung of the lattice once to anchor it.