Assuming all BT Home Hub routers operate the same, you can assign a static IP address to the device connecting (MAC Address).
So the IP Address to the device never changes.
In windows command prompt type in ipconfig /all and look for your wireless adapter and find your MAC Address.
https://docs.google.com/a/iselinc.com/file/d/0B2xyjZTJk1m6cFpXdVZITnBiTnc/edit
Connect to your router via Ethernet cable and enter the configuration settings.
I believe you should be able to click Settings -> Home Network -> IP Addresses,
then assign an IP address to the Wireless Adapter's MAC Address you found in ipconfig.
Optionally you can also edit your Windows Wireless Adapter Settings to match the settings you defined:
Assuming your router's IP address is set to 192.168.1.254 and you assigned your MAC Address the IP of 192.168.1.100.
While other devices will still ask the router for an IP address (DHCP) your PC will have a static IP address reserved on the router that it won't assign to any other devices connecting, and if you statically defined your PC's IPv4 gateway and IP address your PC will always check the same IP Address for connectivity.
This is just a step to ensure your PC is actually attempting to communicate with the router and there are no issues with DHCP, to which the router will simply say, "Hey I know you, this is your IP Address", rather than: "I don't know you, what IP Addresses do I have, here's one that's not being used."