Hopefully someone here can help me figure this one out because it's got me completely stumped.

So I bought a new guitar a few days ago and I've started to notice that mains hum you get when things aren't properly grounded. It's an LP with dual humbuckers so I know it's not just pickup noise. And I know it's a grounding issue because the noise stops completely when I touch anything metal on the guitar or the lead.

Now here's the odd part. Normally I'd assume the guitar was the issue but I've checked it out with a multimeter and there's nothing obviously wrong between any two points. I've also tried it through a different amp and I've tried different guitars through the main amp I'm talking about here. In every scenario there's no hum whatsoever. It's only when I'm running the LP through my JCM800 that I get the buzz and it's really melting my mind trying to figure out where it's coming from.

So... any ideas, UG?
My first guess would be bridge ground. Even though you say you used a multimeter, open it up and check all your ground connections.

Also just for fun try plugging the amp into a different outlet.
pics of gear updated on profile 11/16/09
Just a little update. I've switched out different leads and got the same result. I tried a different wall socket and the hum changes but is still present. Now it's unnoticable at bedroom levels and touching metal parts of the guitar makes almost no difference but as soon as you hit about 2 on the master volume the buzz becomes very audible regardless of where my hands are.

Grounding problem with the amp perhaps?
More than likely you're on a circuit with some appliance or computer or TV that's generating some noise that your amp is picking up.
When you touch the strings and the amp goes quiet that basically proves that the strings are connected to the output Jacks ground, that the cables ground makes it to the amp and the chassis ground on the amp is connected to AC ground.
Moving on.....
So it would seem that everything is grounded correctly then. I've done a few more checks and this is all the information I can gather on my own without taking it to a tech:

If I have the amp running on it's own it's almost totally silent until about 6 on the master volume and even then there's only the faintest background hiss. This would tell me the amp itself is fine.

If I plug a lead into the amp, the hiss is louder at a lower volume but would probably be bearable in a live situation. I fully expected this to happen because the lead would act an an antenna of sorts for EMI. I've tried switching out leads and they all sound identical so nothing wrong there.

I plug the guitar in and the noise gets very noticeable after about 2 or so on the master volume. This says to me that it's the guitar that's at fault but as I said, it's all been checked over and the guitar itself seems totally fine. I get a hiss with the guitar volume all the way off and a buzz with the volume up. So I'm guessing I'm picking up interference from somewhere. That explains the buzz disappearing when I roll the volume back but it's the hiss that's getting to me.

I doubt it's to do with the outlet I'm using because I've tried several all over the house with exactly the same issue. If it was purely EMI then surely it would go almost completely silent with the volume rolled off? So I'm back to a grounding issue but again, the amp sounds fine on it's own but really noisy with anything at all plugged in.

I'm starting to tear my hair out over what I thought would be a fairly straightforward issue to get to the bottom of.
I still wouldn't rule out a shielding problem on the guitar.
If you've got a spare aluminium foil you can try to wrap it around where the electronics are located, then make sure that the foil is grounded, if this helps you need to shield the electronics cavity.

that guitar is like falling in love with a stripper
modded Squier Strats