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Cable Broadband and ADSL are two entirely different technologies. Do not on any account get a router which has an ADSL modem.
Any manufacturer's router with wireless access point should be compatible, with cable, provided there is no inbuilt modem. Some recommendations are listed in
this article.
Connection should be simple enough provided you power off the STB, unplug existing cables, plug the WAN port of router to the STB ethernet port, and the LAN ports of the router (or wireless if you want) to the PC(s). Can be easier to get it running first wired, to set up that configuration, before setting up the wireless. When you repower on everything, you need to point register the connection with ntl serverrs using your account ID PIN and password you already have.
NB moving this thread to Computers & IT