The ESP8266 can act either as an Access Point (Master) like the BT router a station (Slave) like a Laptop.
When acting as an Access point it has a fixed address of 192.168.4.1. In this mode you can connect devices to it, like a Laptop or tablet by setting the wi-fi or tablet built in wi-fi to the SSID of the ESP8266. The ESP8266 will give the Laptop or tablet an IP address in the 192.168.4 range(network). Of course in this mode you will not be able to get to the internet because you are not connected to the BT hub, you are connected to the ESP8266 which is not connected to the internet.
When acting as a station (slave)(menu option 5) the home BT Access point will give the ESP8266 an IP address just as it does any Laptop or PC that you have connected round the house. In your case that will be on the 192.168.1 range (on the 192.168.1 network). In this mode the BT hub will give the ESP8266 an IP address and then the ESP8266 will be able to access the internet because the BT hub is connected to the internet.
Problems:
If when using menu option 5 (set as a station) and then option 3 (info) you do not see an IP address in your network range it is because of the following reasons:
1) The SSID and password is not set to the BT Hub and so the Hub does not know its there (option 3 to check)
2) The BT Hub may take a minute or so to give out an IP address
3) There is built in protection (I don' t know) on the BT hub tht will only allow particular devices to connect (MAC filtering), if this is the case the MAC address of theESP8266 needs to be added to the BT Hubs list (sorry don't know how to do that)