I've walked around the room with the mic in my hand and the headphones on. The sound changes as I move around the room, but not enough to help me narrow its location down exactly . It seems to be coming from all the walls and floor. As if the whole house's frame is quietly resonating to a distant low frequency Diesel engine of some kind. That's what it sounds like anyway.

I'm relatively sure it's not hum in the gear itself, otherwise the noise would be the same as I moved the mic around. Also I've been through several different bits and brands of gear and the noise never changes.