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Connect it to the home hotspot using one of the Ethernet connections on the home hotspot, to the Ethernet port on the PC. Its a waste of a desktop computer if you are going to connect it using wireless.
Did you clone the BT Home Hub wireless settings?
Cloning the home hub settings does not work properly. I would start again, and this time use the separate SSID that the hotspots transmit, do not clone the home hub settings.
Cloning the settings simply confuses wireless devices, and you cannot tell which one they will connect to. The weak signal can simply mean its connected to the home hub, not the hotspot.
If the hotspot has its own SSID, then you can see whether you are connected to it.