In the fuse box did the RCD blow too, or just the 30A fuse?
If the RCD tripped the most common reason is water or moisture getting into the electrics and tripping the RCD.
That said this wouldnt have caused the plug to be covered in carbon, this is looking very much like a poor contact between the socket and plug.
If you have have changed the plug, I would also look to change the socket, as from my experience the socket will have carbon on the pins too, and its normally the socket pins which are not tight against the plug pins which create arcing and hence carbon being formed.
Changing the 13A socket is straight forward to do, and could potentially stop an electrical fire, if I was to guess how you dripped the fuse it would be in turning on the socket you touched the plug or nocked the socket in doing so which created a poor contact.
I just wanted to see if I could be any more assistance?
Can you please advise if you need anything further or if your happy to close this case, please rate my response.