Wow, lots of replies with invaluable information, thank you all
Right, progress update as follows:
I've isolated pin 4 on the UL41, all the waxies and dodgy bits of wire have now been replaced, and the set is showing significant signs of improvement, as it seems louder, clearer, and the original bulbs have come back to life. However, there is still a little bit of a hum and, even though the LW/MW selection switch seems to be working now, I am just picking up patches of static and the vaguest hint of a station on LW, though that might partially be down to very poor reception here in my kitchen, I do suspect that there's still an issue with LW that needs ironing out.
I haven't done anything with the electrolytic smoothing can yet, nor did I manage to make it down to Cricklewood to get the 450V 33uF and 16uF caps. However, I actually have got two 400V 33uF caps sitting here, so I was wondering if I can use them to test things, as per Kalee's suggestion, by temporarily tacking them onto the can's terminals to see if the last hint of a hum goes away, or are they completely unsuitable?
Furthermore, in addition to the wiring side of things, I've also repaired a small split in the speaker with tissue and PVA, which seems to have worked nicely, so, once the hum and LW tuning are resolved, it looks like there only remains a dab of black paint to touch in a few small areas on the dial glass and a coat of white on the bulb reflector plate, and it'll be time to reassemble the radio