The OP mentioned about getting prompts on their TV screen asking if they wanted to accept a connection, I'd have thought this could potentially be the precursor to a password prompt?
As for not being close enough, our neighbour's TV is directly through the wall to ours, a mirror layout. It appears on Bluetooth searches from our lounge quite reliably, so their STB could if it was WiFi enabled... (they have Freesat, FWIW)
To the OP: Assuming you have a Virgin-V6 box, it has a WiFi connection internally built in. You mentioned about the prompt on your TV screen refers to one of your neighbours devices. I could be completely wrong, but I suspect the people next door could be trying to connect one of their devices to your V6 box. Every time they try, the box generates a prompt to say "do you want me to accept this connection?" which is put onto your TV picture. I use one of the (slightly older) TiVo boxes which doesn't have WiFi so I can't check this theory, and it could also be complete balderdash.