Thanks for all the replies. I opted to try and use the existing socket first, and the cables went into the connectors without any problem. I just loosened the connectors off slightly and the new cable slid in easily. I guess I was helped by the fact that the existing cables were coming in at the top of the box and the new one from the side, but screwing the whole thing up again didn't feel any more difficult. All done and dusted and working fine.
