You may have a fault but if you are being asked to sign into EE you are trying to connect to an EE Hotspot.
Disconnect from that WIFI and see if you can see your home connection on the list (Should be near the top) if you are unsure which is your the name is on the back of your broadband HUB (Unless you have changed the name)
If you can't see it then you will likely have a fault and can get some help here:
Broadband and wi-fi | BT Help
