Rega Planar 3 hum resolve.

Rega is stubborn , seldom(never?) change a stand they take .

There is something wrong when a TT  has a cottage industry of after market " upgrades " .

The best fix is to get a turntable not made by Rega. That will fix your problem.

I know this is well past the date the question was posed, but the simplest method is to buy a hi fi rack that separates your turntable for your amplifier. Worked just fine for me when buying  an Apollo Storm.

monko, In this case, the OP had a problem well known to owners of the lower end of Rega turntables; hum that got worse as the cartridge approached the motor.  Ralph offered the standard correct solution.  No hi-fi rack and no amount of separation between TT and amplifier will fix that particular Rega-specific issue.

Bought one last week and was excited. I could hear a faint hum immediately but thought it was a fan in my hallway. Three songs later it was obvious and getting worse. After poking at things, found that it was indeed worse the closer the cartridge was to the spindle. Tried everything I could electrically to fix it to no avail. I even bought a $200 phono amp. Ridiculous to have such a problem. Returned it and ordered a Pro-Ject X2. My AT LP 60 sounded better than the P3. No way I was going to start monkeying around trying to jury rig an internal ground or add shielding to a new $1K component.