DIY wiring in kitchens (in England anyway- Wales is different) is not notifiable but has to be done properly.
First thing- is the existing socket on a radial circuit (20A fuse/breaker at the consumer unit) or a ring final circuit (32A fuse/breaker at the CU)- either type could have 2 x 2.5mm or larger T & E cables coming into it. Or is it a spur from an RFC? You need to find out- if it is a spur then you cannot spur from it UNLESS the entire spur is powered via an FCU.
Second, is the new cable to be chased in or surface mounted? If chased in then the circuit must be protected by an RCD at the consumer unit (an RCD socket is not acceptable since that would not protect the buried cable)
Third, buried wiring straight across from the existing socket to the new socket is fine, straight up or down from existing to new is fine, across then down is not acceptable. If the wire is on the surface then that's fine. The common way round this in a kitchen is to chase drop the wire straight down to below worktop level, run it on the surface below the worktop then chase up to the new socket (or not even chase if it is hidden by a built-in appliance). Because 1 part of the new wire would be buried you would still require RCD protection at the CU.
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