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It would be wrong of us to say that you can move the cable yourself. Ultimately all of those cables up to the connection to the Telewest STB, modem, or the master phone point socket is their kit. If you do alter it., but something goes wrong. your going to pay to get it sorted out. Worse if you manage to get it wrong in such a way that you introduce problems back into the cable network, Telesest are going to be very unhappy.
With the warnings aside, I suspect this all depends on how competent you feel at DIY.
Ultimately if you are careful, given that you already have all the components and are shortening the cable, there is no reason why you cannot relocate it. Just make sure that all the new joints you make are neat and tight, and there is no stray wire fibres that could create any shorts. I relocated my ntl cable to the STB in a similar way a few years ago and never had any real issues.