[Arran]

Interesting, by the pictures you show the leads to the transformer look like they are cloth covered. It also looks like a 25 cycle transformer judging by the amount of iron used in the core. If it was a 25 cycle transformer something must have really gone wrong in that set to burn it up. The good news is that these sets use 6.3 volt tubes so finding a replacement shouldn't be too difficult, there were literally dozens of makes and models of radios that used a similar power supply layout from the late 1930s up until the 1960s, find a junk chassis from a set that used a 6X4, an 84, or a 6X5 using the same number of tubes with similar current demands, ones using a 6K6, 41, or a 6AQ5 as an output tube.
Regards
Arran