I also have Telewest broadband (and a router).
There are two ways of doing what you want, wired or wireless.
Note it may cost you more than �75, but you will be set up if you want to add another PC or laptop to the network at a later date.
WIRED.
Buy a wired router (make sure it is suitable for CABLE not ADSL). About 50 pounds
Buy a length on CAT5 ethernet cable to go from the router to your PC. About 10 pounds
You then need a network card in your PC. Many modern PCs already have a network card so you may have this already. Check the back of the PC. About 10 pounds if you need to buy one.
Here is a picture of the socket. It is NOT the same as your phone modem socket. Note the small diagram just above the socket.
http://www.publicwebstations.com/howto/etherne t.jpg
This is the easiest to set up, but you do have a problem of getting the Ethernet cable from the router to the PC.
If you are able to hide the cable then I suggest going for this option.
Cover wireless on next append.