Buzzing Sound In Speakers

I have a Rega RB 300 tonearm which has been upgraded with RB 1000 wiring (supposedly). It was done by a local dealer a couple of years ago. Last year I sent it to Rega in Texas to be checked out by them. They said a ground wire was not installed properly.
It is mounted on a new Michell Gyro SE. I have an Arcam C31 preamp with P1 mono blocks.
When the pre is set to phono, I get a loud buzzing sound in the speakers when at higher volumes. This is without the record playing. When I touch a certain one of the cables that runs to the preamp from the TT the buzzing gets significantly lower but is still there. Whenever I touch the preamp or TT itself the buzzing lessons somewhat. When the C31 is switched to CD, the buzzing stops...totally.
Could it be that the phono stage in the Arcam is of poor quality and not shielded properly? Wonder if any other Arcam people have had this problem. Thanks so much to all.
Sounds to me like a loose ground wire or maybe a bad phono interconnect cable or just a bad tonearm or cartridge connection..
Do you mean hum? Buzz is a technical term for a bzzz sound, and a hum is for a hmmm sound.
It's more of a buzzing sound at high volume. I ran a ground from the bottom of the tonearm (threaded part) to the preamp and it helped somewhat but it is still there. If I disconnect the phono cables from the preamp inputs the bzzzing stops completely with only a very minor hissing sound at high volume. Thank you.
Post removed 
Well here is the latest in the never ending Buzzzzz saga. I have an old Marantz 6025 TT that I bought new in the 80s. I plugged it into my preamp and... buzzzzz. I grounded the Marantz to the Arcam preamp and the buzzing got better but was still there. I have a Rega phono stage that I had on another system a couple of years ago so I thought what the ...., I'll give it a try. I plugged it into the auxillary of the preamp buzzzzz. It looks like I will have to get a phono stage. I never really liked the Rega phono stage before or now. Any suggestions w/o breaking the bank? A friend told me that a EAR was the best that he had ever heard but that break the bank comes into play again. Thanks to all for your help.
I purchased a used Vacuum State JLTI Phono ( solid state ) and it sounds terrific...Under $ 1K used..Sweet like tubes but no tube hassle...
Thanks Thorman. I have been doing some research on the JLTI. It is definately being considered. Any other recommendations will be greatly considered.