The modern (for 1950s definitions of 'modern') solution to the problem is a thermostatically controlled electric glue pot. Unfortunately hot hide glue is a bit of a niche thing mainly of interest to antique restorers and musical instrument makers, so there aren't many of them on the market and they are horribly expensive. Second hand ones seem to be very rare and keep their resale value well.
So I went looking for a cheaper alternative. I've heard of people using electric baby bottle warmers, however I don't know if the temperature controls on them go as high as 60C (Do they? The adverts I looked at all said meaningless things like, "the ideal temperature for your baby."), and while I was Googling around looking at different options, I stumbled across a forum post where somebody mentioned using a mini electric deep fat fryer. A bit more research and I ordered one of these for only fifteen of your British pounds, postage included. And it's ideal for the job.
I keep the glue in a small Nutella jar (the type that's like a drinking glass with a plastic lid). I made a Perspex disc that fits snugly inside the cylindrical fryer pan, resting on top of the stainless steel basket. It has a hole in the middle that the glue jar fits tightly in, and a smaller hole for the glass mercury thermometer. This keeps the jar from moving around and minimises evaporation from the water bath. Closing the lid when it's not actively in use will reduce evaporation and heat loss even further. The water (filled to just below the Perspex disc) heats up in a couple of minutes (the glue takes a bit longer to warm through), and the thermostat maintains it at the set temperature to within about +/- 2C. The numbers on the front panel are way out, so you do need to use a proper thermometer to find the right setting in the first place (in my case, 60C seems to be slightly over 90 on the dial).
Best of all, it can also make very nice deep fried chips. Try that with a baby bottle warmer! The only disadvantage really is that it takes up quite a lot of space on the workbench, though not as much as the electric hob and pan did.
Edited to add: My earlier mention of electric glue pots being 'modern' in the 1950s was a wild guess. I just got curious about when they were actually invented and did a bit of poking around. Take a look at this patent filed in 1894!
 Various sources on the net recommend glue temperatures of around 60-70C, usually the lower end of the range. I get the impression that it isn't terribly critical. Too low and the open time suffers. Too high and it deteriorates, though time is also a factor. Briefly letting it get up to 90C probably won't weaken it very much but running your pot at 75C all day long might.
 Water continually evaporates from the hot glue, so you have to occasionally top it up to keep it from getting too thick.