The adaptors plug should have been properly rated for 13amps. Or an internal connection failed and arcing started. All the same the plug top should have been able to resist the max current draw of the fuse.
Second look, I guess it could have been arcing on the line connection, maybe copper hardening due to heating up and cooling down.
It looks to me like the adapter has melted but the socket is fine. 13 amp fuses produce a lot of heat at high current draw, so if the adapter wasn't made of sufficiently heat resistant plastic...
The adaptors plug should have been properly rated for 13amps. Or an internal connection failed and arcing started. All the same the plug top should have been able to resist the max current draw of the fuse.
Second look, I guess it could have been arcing on the line connection, maybe copper hardening due to heating up and cooling down.