I initially set up the Airport Express to join the existing network and can now play music via Airplay.
The AirPort Express can "join" virtually any wireless network, but it does not "repeat" or "extend" the wireless signal when it "joins" a network.
However, when I tried to extend the existing network, following the instructions in the help file, I keep getting an error message which simply states that the Airport is unable to extend this network.
"Extend a wireless network" is proprietary setting or feature that will only work with other Apple routers. It is not compatible with routers from manufacturers other than Apple.
As LaPastenagure says above....If you want to "extend" a wireless network with one Apple router.....you must have another Apple router in the mix.
If you want the AirPort Express to provide more wireless coverage for the BT network, you must permanently connect the Express to the BT router using a wired Ethernet cable connection. Then, configure it to "create" a wireless network using the same wireless network name and password as the BT network.
Ethernet cable can be run up to 330 feet or 100 meters with virtually no loss, so you should be able to locate the AirPort Express where it is needed.