I once owned one of these lathes but my memory of its details are hazy. I’ve also similar problems with refurbishing my dear little EW lathe, smaller and simpler than the Drummonds.
Nevertheless, are the bearings plain bronze bushes pressed into the casting? If so…
1) Investigate sintered bronze equivalents, made as standard commercial items. (“Oilite” is perhaps the best-known make; most transmission-parts stockists sell them, e.g. HPC Gears, or Bearing Boys.) The lubricant is an ordinary, light oil.
Note though that these cannot be machined, or not easily. Attempting to modify the bore will damage its lubricating abilities. Holding it safely without distortion or cracking would be problematical, and the material is quite brittle.
This may not work if the spindle itself is significantly worn. In that case it may best ground to suit the nearest smaller available bushes – which might need be metric (quelle horreur!) to minimise the reduction. This may also introduce difficulties of its own, with the diameters of the areas of shaft that hold the pulley, back-gears and change-wheel driver pinion.
…
2) You could probably make new bushes on the same lathe, with care!
Dismantle the lathe to measure everything.
Make a plug-gauge – brass, mild-steel or aluminium – to test the new bushes’ bores.
Use leaded-bronze; machine the outer and inner diameters without removing the material from the chuck so they are truly concentric; take light cuts to avoid problems from the wear making the chuck “jump” (you can see that happening if the wear is heavy).