Given you imply the socket is in the kitchen, this work is notifiable in advance to your LABC under Part P (see the wiki for details, basically you have to pay them a notification fee). They are then supposed to do whatever inspection and testing they deem necessary...
Assuming you have a standard ring final (I hope so given you say it's a 32A breaker), then if it is a spur for a double socket off an existing socket, 2.5mm T&E is almost certainly what you want (however, I can't say this for sure without knowing the route the cable is going to take etc).
Note that your new socket must be protected by an RCD under the 17th edition of the wiring regs, so if your existing circuit is not, you will need to ensure the new one is, either by installing RCD protection on the entire circuit, or perhaps installing an RCD protected socket. Also note that any cables buried at less than 50mm from the surface not in earthed metal conduit must be protected by an RCD, so you can't necessarily just install a protected socket.
Finally, given that LABCs normally charge over £100 as a notification fee, for a single spur like this, you may be better off just getting a
competent person who can self certify in to do it - it'll probably cost you about the same overall, but you'll know you have a professional job done...