Electric Range Keeps Blowing its Fuse
As gbulmer pointed out, the plug is wired incorrectly.
That plug is damaged, I would replace it.
Trim back any damaged wire (with burnt insulation) and make sure the earth wire has the most slack (so it is disconnected last if the cable is pulled out of the plug).
A typical electric hob ring can need 1.7 kW. Two of those would overload a 13A circuit.
I would check the rating of the electric range. High current appliances of that sort are normally connected directly to a dedicated 20A or 32A circuit using a switched wiring box, not plugged into a normal ring-main using a normal 13A plug. If the 13A fuse is overheating or blowing it suggests the range is overloading the socket. I would consult an electrician.




In my home, I have a 32A circuit that feeds the separate electric oven and electric hob (4 rings) - each is connected through a switch as shown above (one labelled "hob", the other "oven"). Your "range" probably needs a dedicated circuit and isolating switch.