There hasn't been a short circuit just an overloaded fuse, so it wouldn't trip at the consumer unit.
Change the socket face and throw that heater away....well thats what I'd do.
It looks like the yellow is the live but...
I don't like the way the single insulated wires are going through the metal, if you wanted to use it youd have to earth all the metal parts.
Might be best to buy a new light.