I'm with tube fanatic and JJKIZAK on this one. I think the physical location of the wiring ("lead dress") is at the root of the problem.
Does the hum occur if nothing is connected to the amp inputs? How about if RCA shorting plugs are connected to the inputs?
Once it is certain that the amp (not the interconnection of the amp with other equipment) is humming, try this:
Connect amp to speakers. Connect shorting plugs to amp inputs.
With amp upside down, move wires around with a non-conductive tool (plastic ballpoint pen barrel?) and see if you can change the loudness of the hum.
The lead dress as it stands now does not appear to be optimized for minimum hum, so it could be coming from any number of sources and pickups. The power switch wiring and the filament wiring, as mentioned by others are likely culprits.