Your BT router probably has a built-in modem. Where as the NTL routers usualy don't. So you will receive a modem from NTL which plugs into a router. Your BT router/modem probably plugged straight into the phone line. The NTL modem plugs into a fat cable (fibre optic). Different plug than a phone cable (its round). Then you connect the modem via an Ethernet cable to a router. The router then connects to your PC's. But you already knew that bit.
So basically, you need to buy a new router, or tell NTL you are going to terminate the contract and go elsewhere unless they supply you with a free wireless router like I did.