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Right, a few bits of information.
The TV is a Samsung UE40ES6800 LED (Sept 2012, so older than I thought (aren't we all)). But it does seem to have Bluetooth - at least when I go to Bluetooth on my adjacent computer, 'TV Bluetooth' does come up, although not sure what to do with it.
Plugging in a 3.5 plug to the TV's headphone socket does turn the TV's speakers off. In normal circumstances, this is how we connect the TV to the sound system (amp, speakers). This does of course cut out the TV's (rotten) speakers, and give us decent sound through the system speakers.
Any ideas how I can establish what the 'Bluetooth TV' does in fact connect to? I suppose I could try linking it to a nearby Bluetooth speaker...
A