How would I connect and be able to ping a 10.10. ...... wifi device via my BT Hub that has a gateway address of 192.168.1.254?
With IP starting 10 suggests a connection to the BTWIFI network from your BT hub. This broadcast from hub but is not a problem and connection do not have access to your home network . This can be turned of in MYBT but you lose access to BTWIFI when you are away from home
If you have a 10.10 device that is connected to your WiFi, the changing the ip address on a PC or pad etc. that is connected to your network from 192... to a static 10.10.x.x address would allow you ping that device you want to.
All 10.x.y.z addresses are private as such you will not be able to ping them over the Internet.
A little more information about what the objective is might get you a more detailed answer.