[Arran]

I don't want to be the bearer of bad news but I would inspect the power transformer, and the filed coil on the speaker, before getting too ambitious. If the filter condensers, or the wiring, had a dead short that can cause the rectifier tube socket to burn as well. What does not make sense is that the #80 rectifier tube, other then obviously having the glass smashed, does not look like it melted down inside. I can't help but notice that one of the plate pins on the #80 is missing, so clearly the socket burned up with the tube present. As for replacing the four pin socket I would measure the diameter of the hole, and the spacing of the rivets and make a note of those for your search, they are not all the same. You could also use a 5Y4 or 5Y3 in an octal socket, but then it won't be originals, and #80s are not generally difficult to find.
Regards
Arran