At the moment the socket in the kitchen should have 2 x cables as part of a ring circuit (check this 1st).
On the assumption that it has, you need to disconnect one of the cables and via a terminal block connector, terminate it inside the back box and extend this cable down to the new socket through the wall.
To complete the ring again, you then need to run another cable between the new socket and the existing socket. This cable will terminate on the socket in the same positions and the cable you removed and extended down to the new socket.
Simple diagram where ----- = wire and N = new socket and O = existing
Current set up -------------O-----------------
To be set up ---------O----------N--------terminal block--------------
Make sure you position the terminal block so that the socket face doesn't foul it when re-fitted, tape it up for safety.