[Arran]

Matt;
Some battery sets had an electrolytic filter cap in the B+ line, and if those fail you can end up with a hum no matter how good the battery eliminator is. They were typically of a small value, but rated at 150 VDC, this Philco does not have one of those, so the hum may be caused by a tube shield being left off. It also appears to have a number of large bypass caps contained inside a can under the chassis, they will need to be replaced eventually if you intend to use the set regularly.
Regards
Arran