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I assume you mean the cable that goes from the socket to the radiator. If the internal cable that goes from the fuseboard to the socket has no earth/CPC (circuit protective conductor), that is a big no no and needs to be rectified.
More likely however is that it’s the cable from socket to the radiator only has 2 cores (a live and a neutral), and providing the radiator is double insulted (meaning that there is extra non conductive material between any of external metal parts and live parts inside) it is totally fine. You’ll often notice that on some plugs the top and longest pin for the earth is actually plastic, which is the case when the cable is 2 core and supplying a double insulated accessory. If you look for a sticker on the radiator, I should have the square inside a square symbol on it, which indicates it is double insulated.Honestly my guess would be that something, like fluff or dust buildup had fallen on the heating element and ignited, rather than a more serious failure of a heating component (but that is just a guess).
We had a terrifying moment with the radiators we had fitted last year. We have electric radiators as we do not have gas supply.
In the middle of the night the radiator in my son's room started flaming / sparking from the core with debris falling out of it and syngeing the carpet. If I had not been able to switch it off quickly it would have caused a fire I think.
The manufacturer/ retailer have been very helpful in customer service and it currently being sent back to evaluate what happened.
However, when an electrician came today to remove it he said it only has a two wire cable, with no earth. Can any electricians ( @Nef maybe?) advise whether this is illegal / doesn't meet product standards?
My concern is we have five other electric radiators of the same model fitted in the house.