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#11
A so-called Router like the BT Home Hub 5/6 contains several functional parts.
Each part is configured separately from the Web interface as accessed from your Web Browser.
1. A Modem (ADSL).
2. Router (Ethernet and/or Wireless).
3. Wireless Access point (Wireless hardware).
4. Hardware firewall.
1. Is the connection to your ISP.
2. and 3. are your internal network.
4. Separates Your internal network (LAN), from the Internet(WAN).
If the Modem is not connected you get is an indication in the Web page for the Internet connection.
In your case the BT Smart Hub Manager.
The other functional parts still work.
There are plenty of guides on YouTube e.g. Web admin interface of the BT Smart Hub (BT Home Hub 6) router. How do you turn off wifi? - YouTube