UPDATE:
The bathroom light is a standard incandescent lightbulb.
Using a quad shield cable to connect the TV to the antenna socket on the wall did not make any difference.
There is also an outside light (incandescent) that when it’s switched on, causes a smaller amount of continuous interference for as long as it’s switched on.
Sometimes muting the sound on the television can fix the interference problem(!!) (The audio is not being routed through any special stereo or speakers etc, it’s just standard sound straight out of the TV).
Does it now seem most likely that the problem is the antenna cable (in the wall) is running too close to the electric circuit?