z1812
Thanks for your reply. The problem is with my Les Paul Traditional. It has Classic 57 hum bucking pickups. The interference changes depending on which way I face although the same facing does not always eliminate the hum. I tried a ground loop isolator between the Guitar and Amp but it didn't work.
Nice to see all the replies. Hopefully a good resource for people with similiar problems.
There are a few ways noise can get into a guitar such as that. The pickups themselves are a humbucking design, but unless the two coils in each pickup are extremely well matched - and sometimes they are and sometimes they're very close but not quite there - a very little noise can still get through. High gain playing can amplify even that to the point it's a problem.
The more likely route for noise to be picked up is the wiring from the pickups to the control cavity and the wires in the control cavity itself, which combined with the controls act as a primitive radio receiver. The best answer to this is to thoroughly electrically shield the control cavity. Shielding material is usually either a thin copper sheeting formed into the cavity and glued to the panel that covers it or a conductive paint.
Gibson may already have applied conductive paint, but may not have done the job as well as it might have been. If conductive paint has been applied there may well be a screw holding a wire to the body inside the control cavity, the other end of the wire will be soldered to a potentiometer or the output jack ground connection. Copper sheet will be obvious.
Even if shielding paint was put on at the factory a second coat won't do any harm. It's not cheap stuff, but works pretty well. There are loads of videos on guitar websites and Youtube that will guide you through doing it if you want to do the job yourself using either copper sheet or paint (paint is easier). If you want someone else to do it, most guitar techs are up to the job and it shouldn't be too expensive.
Another option might be active pickups, but that involves quite a bit of expense and work and will alter the sound and feel of the guitar.
Other possible problems are the guitar lead itself. Don't use cheap cable, use a good quality one specifically designed for guitar by a reputable company such as George L's, Planet Waves, Klotz La Grange. No need to spend too much money, and anyone who tells you you need a massive, complicated cable or an expensive one specifically designed for a particular type of music is best ignored. You don't. Use as short a lead as you can get away with as well.
Pedals and amps can also pick up and amplify noise, but there's often not a lot to be done about that, unless you have the kind of money Pete Cornish charges for hum-resisting effects.
If all else fails, noise removing software applied after recording, such as Adobe Audition or the Izotope noise removing plugins, can do a pretty good job without wrecking the guitar tone so long as you use them moderately.