ok... so fcu has 13A fuse in it, presumably.... and regs say you can have as many socket outlets on a FUSED spur as you like, with a load not exceeding the 13A....
A washing machine and diswasher will both be circa. 10A each... so if you only have one on at a time... it should be good. However, if both are on together, or anything else plugged into the socket above... you could be stretching the 13A beyond its limit for some considorable time. (it will not instantly blow at exactly 13A.... it could take 14, 15, 16A for an extended period before finally giving up.... and heating up as it does)
Another possibility is a loose connection behind the FCU... a very high load passing through a loose screw can cause arcing, heating, and eventually damage caused by the heat... which could result in a fire.
It is highly recommended that large appliances be on their own radial circuit nowadays. (over 2kW load), but if impractical, then having them each directly plugged into a single wall socket is preferred. Absolutely not through an extension lead.