May be a silly idea, but are both circuits on RCD?
I suffered a similar problem quite a lot of years ago and gave up in frustration trying to solve it, eventually putting it down to my audio system being "home brewed". In my case I couldn't attribute the source to one item.
Eventually I updated my panel to an RCD one, incidentally discovering a neutral earth short half way round my ring main. Doh! It was a neutral wire knicked by the faceplate screw. Once fixed, the audio system problem disappeared.
I believe that the currents circulating between the short and power source behaved like an hearing aid loop system, radiating at low frequency around the house and picked up by the stereo.
