The BTWifi signal only has a short range of a few tens of meters so it can drop out very easily. There is nothing you can do to boost the signal or if the owner switches off their hotspot.
The BTWifi signal and the Homehub signal are two separate networks.
The owner of the hotspot can check on their Homehub and see that something is logged onto their Homehub's BTWifi signal but they have no way of knowing who it is or what they are accessing on the Internet.
Likewise anybody using the BTWifi can not access the hostspot owners private home network when logged onto the BTWifi signal.
See link
http://www.btwifi.co.uk/help/common-questions/index.jsp