You're pretty much correct. I've found that switching the modem off, then swapping the machine and powering up with the new nic in place does the trick.
Their hinder^Whelp pages suggest releasing the dhcp lease before doing that but I've never found it necessary. 'ipconfig /release' on a win2k box.
You know that you can register MACs directly via the webshite ?
Check with the working machine and have a look at http://selfcare.blueyonder.co.uk/PInfranetServlet?page=p_list_mac_addrs&loadBean=yes
You'll need the username and password that they sent you when you signed up. It's *much* quicker than talking to the helldesk !
i've found the following site about Telewest and NTL cable modems very useful:
http://homepage.ntlworld.com/robin.d.h.walker/cmtips/index.html
(http://homepage.ntlworld.com/robin.d.h.walker/cmtips/swap.html#swap concerns the DHCP release/MAC address issue)
Michael.