Hi Gryph,
Thanks for the update, it shouldn't be a ground issue as the Beolab speakers aren't grounded (they use a 2-core mains lead without a ground wire). The results from the Line In sockets of the TV are best ignored, as these are likely to give spurious noises if the speakers are connected directly to these sockets in most situations.
Please can you try a good pair of headphones in the TV Audio Out socket to see if they also produce the high-frequency whine?
Kind regards, Steve.
Location: The cable workshop, England
My B&O Icons: