Just had another thought......
The outbuilding is currently wired up for NTl broadband. The cable comes out of the set-top box inside the house, into a socket on the wall, then out the wall and into the outbuilding. It then terminates in another socket inside the outbuilding which then connects to the PC.
Is that just a simple RJ45 style connection? In which case, I'm all wired-up, tested and ready to go!!