[SMHarman]

have you registered the MAC address of the router on the TW network, or spoofed/copied the MAC address of the laptop to the Router. IMHO that is what the problem is here. The router is not recognised as a piece of kit on the TW network as it has never been registered to the network.
This would be the problem in the NTL network world and as the TW one works on similar technology I imagine the same problems arise.
While logged on to the router with the laptop you should be able to tell the router to copy the mac address of the PC. Do this save the change - also make this a wide open insecure network broadcasting the SSID - this is easy to connect to - once it is all working you apply security; powerdown everything and then power up 30 seconds later - Set top Box (wait untill fully operational - couple of minutes), then router, then PC.
Should be in action.

I've never heard of a router not working with a network. There was one that was being kicked off networks due to a fault in its firmware resulting in it requesting a new IP lease every 30 seconds and flooding the network with such requests, but thats all I can think of.