Better yet, buy some Home Plugs, and use your spare BT router as a wireless access point plugged into the home plug.
INTERNET --- ROUTER --- HOMEPLUG :::::::::: HOMEPLUG --- SpareROUTER
If you set the spare router up with the same SSID and security key, but different channels (e.g. one on 1, and the other on 11), you'll have a "poor man's" wireless distribution system. Once you have connected to your main router wirelessly, then when you go into your room, it will find the stronger signal on the spare signal, and the wireless configuration is identical, it will connect to the stronger signal.
Ol.
BKP