You need a "stand-alone" Wireless Router, often described as a Cable/DSL Router. Don't confuse the reference to DSL with a combined "Router/ADSL Modem" which is *NOT* suitable for use with Telewest Cable.
<<< Do I need to do anything with my desktop PC which will remain with its wired connection (at least for the time being)? >>>
Not if you currently connect to the Cable Modem by ethernet. If you connect by USB, you will need to change to an ethernet connection between the PC and the router, which means the PC must have a network adapter installed.
<<< What do I need to do about security of the wireless network or is this built in to the router? >>>
The router's Wireless settings will include options for encrypting your wireless connections and MAC address filtering, which lets you select which network adapters are allowed to connect to the router.
I use this Buffalo wireless router with Telewest - click here
Other suitable models:
Belkin - click here=
Linksys - click here=
D-Link - click here=
Netgear - click here=