neatest solution, IMHO: is to chase out the wall & put a new 13A flush socket (coud be a double) at the new location (with a proper metal back box) , run a 2.5mmsq cable to the old outlet plate (or is it a 13A socket??). Then replace the old socket with a connection unit plate (these are ususally used to permanently connect external flexible leads into the mains circuit). This connection plate could be a 13A fused connection unit if you have any doubts about where the ultimate connection to the ring is made. You aren't allowed more than one socket (single or double on a spur unless the spur is fused.. Putting in a FCU means you don't have to bother checking compliance with that rule.
Alternatively if you have access to a cable crimping tool you could crimp the cables in the old box to the new extension 2.5mmsq cable and just insulate them & fit a cover plate, however if you do that you do really need to establish that you aren't overloading the spur.
BTW if this is in your kitchen the part pee police should be notified.
HTH