Mixerboy wrote:
Is there any reason why the hi-fi in the other wood would/could be broadcasting?
Faulty (or absent) EMI filtering is the most obvious answer, but it could be a whole host of things, including the hi-fi's power cord acting as an aerial (which does happen in some circumstances). Lots of consumer electronics devices generate electro-magnetic interference, and there's a lot of different ways in which they can do so. And if it's at just the right frequency...
I'm not an expert in this field, but I do know that it happens, and it seems like the most logical explanation. Quick test: connect/jump one pickup's wires direct to hot and earth on the jack socket, plug in, and see if the problem has gone!