Here is a few useful definitions taken from the wiring regs (17th ed).
Appliance, An item of current using equipment. (note not hard wired).
Circuit, An assembly of electrical equipment supplied from the same origin. (hard wired installation that you have not changed or altered).
Cold tail, The interface between the fixed installation and a heating unit. (i think it can be used in your case. The cable coming from the cooker to the cooker connector is not classed as part of the fixed installation).
Connector, The part of a cable coupler or of an appliance coupler which........ to be attached to the end of the flexible cable remote from the supply. (the cooker connector that is part if the circuit but you have not altered the circuit by connecting the cooker).
Design current, The magnitude of the current to be carried by the circuit in normal service. (eg you didn't overload the circuit be putting in a higher rated cooker).
Fault, A circuit condition in which current flows through an abnormal or unintended path. (you have not created a fault)
Testing, Implementation if measures to assess an electrical "installation" (you have not installed any circuits, you have just plugged in 2 appliances and connected a cooker).
Instructed person, A person adequately advised or supervised "by skilled persons" to enable him/her to avoid dangers which electricity may create. (you are not a skilled person with the respects of electricity and its not your responsibility).
If I read your posts correctly you have not done anything wrong. A little bit more info on the cooker would be nice, what was the current rating of the old and new cooker? What is the complaint word for word made against you?
Think I speak for most of us on here when I say that we will help you as much as possible to get this CHANCER off your back and so you can continue trading. Good luck and keep us informed.