I have used a "wired" Belkin Router in conjunction with a separate Belkin Wireless Access Point. I have also used a Buffalo 802.11g router, all with Telewest/Blueyonder. When setting up both of these systems, when it got to the point of checking the internet connection, it failed. If I ran the Setup again just now, it would still fail the check!
That didn't stop the router from working though. As long as you have configured it to use a "direct" connection, and you powered the modem off for a few minutes before switching it back on and then powering on the router, you should have internet access. With Cable broadband, there really is nothing to configure and no dialup type connection to establish, it's just the same as plugging directly into a network.
You can check in the router's Setup pages if it has got its IP address from Telewest and your PCs should have IP addresses in the 192.168.2.xxx range.