The switchbox in the cloakroom turns off the cooker entirely.
I've just dismantled my cooker from its current location and there are 3 wires, exactly the same thickness and type in the rear of the 3 pin socket at the new location.
It sounds to me like you may have a 32A cooker circuit. If the house is newly built to a good standard then it will be wired in 6mm. If you have a look at the size of the wires behind a light switch; a socket; and the cooker socket, you should be able to see how the wires are increasingly bigger on the higher-rated circuits. If you can get to a hardware shop and buy the smallest possible length of 6mm cable (it might be a metre, but you may find a co-operative assistant will let you have an inch as a free sample) you can compare it to the size of the cable in your outlet and see if it is the same.
It is not unusual for people with a gas cooker, or a dual-fuel cooker, both of which only need a 13A plug, to convert a cooker outlet plate into a socket.
You can get a new cooker outlet plate for a few pounds, and fit this in place of the existing 3-pin socket. You will find it has very big terminals inside and can be connected without the white plastic cover being fitted (you put the cover on afterwards to safely cover the connections).
It is absolutely essential for this that the cooker circuit has its own dedicated 32A MCB, nothing to do with the other sockets, and that it is wired in 6mm cable.
If you are not sure about any of this you should be able to get a local electrician to check and connect it for his minimum charge.