Hi John,
I would have posted earlier had I seen this thread. I presume the wall insulation is the stuff that has the foil layer hence the problem. There are a couple of extra suggestions.
Is the room really a Faraday cage or do you actually have wireless channels clashing ? An app such as "WiFi analyzer" on a tablet device will show up any services from your neighbour fighting for the same channel. A reboot of your BT hub may cause it to select another channel.
Can you move your router to give you line of sight through a window or doorway ? I solved a problem in my house where the wireless has to deal with a 6 foot thick wall by placing the hub "just so". If you have Cat 5 cables to your hub then I presume not.
I hope all goes well.
Brian