Most Telewest contracts your stuck for a year thats why tech support don't care if you threaten to disconect in the long term your going to be better off trying to resolve the issue. You could try phoning tech support again and hope you get someone who is willing to give you some information about what the issue could be if their refusing to send out a tech that will mean its nothing wrong with the modem, so in other words nothing wrong at their end so their not obliged to send out a tech. Did the person you talk tell you what the problem was?
If your getting slow speeds things to look out for are,
1. Routers/Wireless networks if you have one try pluging the modem directly into the computer, reboot your cable modem (power lead out for 10 seconds back in) then see if your speed increases.
2. Firewalls, do you have a firewall? if you don't skip straight to No. 3 thats probably going to the issue. If you do have a firewall try turning down the settings or turning it off all together and see if that improves the speed.
3. Check for spyware, if you don't have a spyware removal tool try going to start, run, cmd, you should get the command prompt, type in netstat -a this shows all the connections going in and out of your computer check for anything suspicious. Also try typing in ping
www.bbc.co.uk in the black box and see what your av time is it should be below 30.