"Hum" is generally used to refer to a 60Hz or 120Hz pure tone. Do you really have hum or what is more loosely defined as "buzz", which is a mixture of frequencies?
Assuming this really is EMI and not a grounding problem, a Faraday cage may work, but by definition, a Faraday cage must totally surround the shielded component and be grounded. That would make it impossible or awkward to access the controls on the Rega preamplifier. If just putting the Rega on top of a shielding material works, that’s great, but it’s not a Faraday cage. Maybe easier to open up the chassis and install a shield inside, once you figure out the source. Anyway, I think this is a solvable problem and not a reason to discard the unit if you otherwise like it.
Or, if the amplifier can be shown to be the source of EMI that disturbs the Rega, it might be more practical to shield the amplifier, since you don't have to fiddle with it all the time.