You should not need to select a pair from the four live and neutral wires.
In a ring main the incoming live is always connected to the outgoing live, the incoming neutral is always connected to the outgoing neutral.
To add a second socket on the opposite wall you connect a new cable to all the existing cables - so you get three reds connected, three blacks connected and three greens connected.
With the new colours, a newly purchased piece of twin&earth would have brown for live (connect to both existing reds), blue for neutral (connect to both existing blacks) and bare for ground (cover with green/yellow sleeve and connect to both existing greens). Any connectors you use need to be rated at 32A.
At no point do you separate out one red and one black as a pair. Separating them from the others would split the ring and could cause overheating and fire in one leg of the broken ring.
Diagram by Ali@gwc.org.uk - used under Creative Commons Attribution-Share Alike 2.5 Generic license.