The OP said it was the UK square open plug that overheated and melted, not the end that plugs into the unit.This is a common and well recognised problem with the Brewzilla.
Recommendations of remove the socket and hard wire quality cable direct seems to be the consensus. Or a properly rated socket for the current.
You should periodically check inside the plug to make sure there is good contact between the fuse and the fuse holder, also that the metal ends of the fuse are not tarnished. All AIOs draw close to the maximum 13A rating of UK square pin plugs, if there is any tarnishing, and hence resistance, between the plug pins and socket or between the fuse and fuse holder then heat will be generated.