Yes, you can only video one Telewest channel at a time (you should be able to record channels 1-5 whilst watching another cable channel - and vice-versa - though).
I should think your VCR can be programmed to timer-record when your parents are out. To record a Telewest (I mean a none channel 1-5 channel), set the video to record channel 6 (or whichever channel gets the Telewest box signal), and set a reminder on the Telewest box to change channel just before your video recorder begins recording.
Telewest probably won't want to know - they're giving you a service, and you're paying them for it. Places like this are best for decent explanations (the above one might be a bit hard to follow!), because it's all written.