By the sound of it and If had the problem, my way would be to get a short length of Coaxial cable, copper foil sheathed with a foam core, ( normal tv coaxial RG59 is no good) dissconnect the cable that runs upstairs from its connection to the splitter in the brown outside box. run the new cable from the brown box to the location you need, fit each end of the new cable with an F plug. (from maplin for instance, F Type Connectors, code FU04E)
Ntl use a crimped on F plug, but a screw on one does the same job.
Connect to the splitter with one end and to your modem with the other.
That way your upstairs cable remains intact for when you want to swop back.
Maybe you should'nt fiddle with the boxes, but I have a habit of never doing what I am told !! Anyway the Ntl installers did'nt mind me having already put in my cable runs before they called, saved them a lot of time.
But thats my way, choice is yours..