tbh it's a bit silly to bother doing this, considering how cheap circuit breakers are.
Your oven is a 13 amp FIXED load, so basically it means you are only going to leave 3 amps for the socket. Whilst it is still not illegal (ie it becomes a 16 amp radial) , it is asking to be overloaded - especially in a kitchen environment.
All someone needs to do is plug in a kettle/ dryer/washing machine/or some other large load, and the mcb will trip. OK Maybe not instantly, but pretty soon, especially if you are cooking at the same time!
If the breaker is hard to get hold of, then I suppose you could replace the cooker switch with one that does not have a socket and use your 16 amp breaker for just the oven circuit.
Incidentally, what is this new ring you have put in? I'm assuming it's a new kitchen ring? If so, then there's definitely no need for that socket on the ccu anyway.