OK. Remember the two things I said early on - firstly that the cable run must not fall below the level of the bottom of the sockets or above the level of the top of the sockets and, secondly, that the new buried cable (and possible the 'new' socket, if it is considered to be 'new') will require RCD protection. That will probably mean arranging fro the whole circuit to be RCD protected (perhaps by having an MCB in your consumer unit changed to an RCBO) - otherwise you would have to install an RCD FCU where the new buried cable originates from the ('left hand') existing socket.