Ahhh.... a mental image begins to form...
If you could make a comparison to the noise you are hearing presently, (where you are), to the noise you hear in the rehearsal room, are they similar?
I'm seeing a lot of variables with what you describe in the rehearsal room, i.e. neon signs, refrigeration units, small appliances, house sound systems, dance floor lighting systems, and Juke boxes, or house music systems. With the businesses, there would be usually Flourescent lights, servers and network systems, possible an HVAC system in the building. In the automotive shops, there would be air compressors and maybe Halogen light stands, not to mention any electrical power tools and diagnostic units.
If the circuit you are plugged into connects with any one or a combination of any of these things, this could be what is causing the noise you are hearing if you are on the same circuit. Keep in mind, that I'm just trying to consider the possible causes for your noise issues from across the pond here, because it reminds me of a similar and very weird situation I had once many years ago at one of the places my band was playing in.
I was at a sound check at one of the pubs downtown and was using my smaller rack rig at the time which was the MP-1, MT100, Digitech DSP128, dbx Noise gates(2), S-1000, and Digitizer4, with a Dunlop Wah, and MXR Phase 90, and MC-1 controller and a couple of FS-2 switches on the floor, through an old Fender 2x12 cab with Altec Lansing speakers. As we started to sound check, I had this obnoxious low end buzz coming through my rig, that I just couldn't get rid of. I thought maybe something was going bad one of my units, since this is the same pub that a couple of years earlier, fried both of my dbx noise gates when I played there without a Furman power conditioner. (I've never played without the Furman since then).
Let me give a brief description of this pub. Originally, it used to be a neighborhood beer garden as we call them here, located on the corner of this city block, that over the years, the owner bought out the next two buildings beside it, and knocked out the connecting walls to expand the pub. At his point in time, he only had the one building next to it, which was where the stage was situated at. As I walked from the stage to the part where the original pub was, I had my guitar still strapped on, ( I was using wireless at the time), I noticed the buzz got louder. I was going to call home and ask my GF at the time to run my stand by rig down to me, because I thought something else had fried in my rack. As I would get closer to the original horse shoe bar, that buzz would get VERY obnoxious! Keep in mind, these use to be two separate buildings that were later remodeled and joined together. I asked the owner if I could come behind the bar, and when I did, it got louder. I looked around at what I was next to, and behind me was a neon Miller Genuine Draught sign, plugged into the wall with a wall-wart AC adapter. I reached down and pulled the wall-wart out of the wall, and my rig went dead silent. I turned up the volume, and hit a chord, and it sang like it was just out of the box! The owner and I just looked at each other, completely amazed at how that affected my amp from across the pub. Naturally, we left that unplugged that night, and played a great show, and sounded totally wicked!!!
There is no way the two circuits should have seen each other, but somehow they did. I don't know if this is any kind of help with your current situation, but sometimes, the weirdest things that seem completely unlikely can actually be a problem. I believe it's possible, due to your particular gear set up, that you might be running across something similar to that situation. Being a guitar player, I never imagined I needed to be an electrician too, but having a fundamental knowledge of electrical wiring and household circuitry certainly doesn't hurt.
It helps me to be observant of what's being used around me, and being aware of what else might be plugged into the circuit I'm connected to, to try and resolve noise issues without having to spend a ton of money on expensive gear. It sounds like your rig is sensitive to other things in the circuit just like my rack can be at times.
Harley
I was typing this while you were posting all the sound clips. Definitely a bad ground loop is what I'm picking up from it.