I am not familiar with that Rega, but does that Rega turntable have built-in RCA cables?? I would also suspect a worn out cable, possibly at the RCA plug, especially if the cables are old. With the turntable on, try giggling the wires at the RCA plug and twisting the RCA plug and see if the hum goes away or gets worse. If so, replace the cables, or at least the RCA plugs on the end of the existing wires. Same goes for the ground wire as Sean suggests.
apt holman problems
I recently bought a rega 25 and tons of albums -- the good news. The bad news occasionally the right channel cuts out and I reconnect everything and will try some connection cleaner. Now a hum has begun in the phono stage, seems worse on phono 1 than two. I don't have a manual, but might it be a ground issue? Is it worth trying to fix or is it time to get "tubed." Other components are Adcom 5500 monoblocks with Vandersteen 2ce's. thanks.