Got a brand new Home hub 2 few weeks back now and noticed using the BT App couple of rogue connected devices appear on the list when I check and appear to be from my absolutely odious neighbour's. I'm bit baffled as obviously as the devices suggest they are Wired and ones a Laptop and another's a phone but I'm confused as to how this is happening when I've a brand new Network and Password.
Is you house a semi detached to your neighbour and do you use Power Line adaptors on your network?
In theory powerline adaptors shouldn't work across consumer units, but sometimes they do. Again your neighbour shouldn't be on the same electrical phase as you, the 3 phases should cycle along the street thus anybody on the same phase should be far enough away for the powerline adapters not to talk to each other, but if he is your electrical wiring is talking to his electrical wiring.
The powerline adapters should be using different encryption codes, so although they show up on the BT App, there should be no actual data being transferred, but they may interfere with each other. Its unlikely they are using the same code as yours, but if they are cheap units, that may be the case.
It a bit like wireless networks, you may be able to see another network name, but assuming its a secure one, you would not be able to connect to it.