Must be some electrical magic.
Nope! What happens is this, we are using alternating current, this means that the voltage rises and fall at a rate 50 times a second. 240 volts is an average of those rises and falls. The rapidly rising and falling current produces a similarly rising and falling magnetic field, place a coil of within that magnetic field and a voltage will be generated within that coil.
Leaving an extension lead coiled up places the coiled up lead within that magnetic field, producing another voltage beside your 240 one.
I've seen extension leads catch fire under these conditions, and as the heat rises, so generally does the current, and so does the magnetic field, and so does the current---.
Replacing a 13 amp fuse with a bar is frowned on, but if there are any other retired sparks out there they will point out, as I do, that the 13 amp plug was preceded by a 15 amp plug that had no fuse, BUT they were radially wired, not used on a ring main.
By all means replace the fuse, but then run a dedicated power line to your consumer unit and connect to a 20 amp MCB.
Connecting to a ring main normally means that the MCB is rated at 30 to 32 amp, this is not good!