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Couple of things worth clarifying / checking first of all:
Disconnects can be a result of the upload stream being saturated, Are there any prolonged downloads (P2P filesharing) running?
You have tried Zone Alarm settings. Can you confirm you also have a current antivirus and antispyware protection in place?
When you say you turn the computer off and reboot, do you also have to reboot the router and modem, or just the PC. If it's just the PC, it is unlikely to be an ntl based issue.
Does the problem repeat itself if you connect a PC direct to the modem, without the router?
I'm not trying to point the finger at your network, indeed direclty the opposite, it's just that needs to be ruled out, so as to confirm the problem lies in the modem or ntl network.