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What specifically melts on extension leads then? Is it the plug overheating due to a poor connection between the pins and the socket, or is it because people leave the extension lead coiled up and it cooks itself? I thought our UK plugs were designed to take a continuous 13A, not max/peak for short periods.

Incorrect.

I asked on two electrician forums (one linked earlier in this thread) and the view was: 13A is max load, and it is not anticipated that this is continuous.

13A is typically 230v * 13A = 2,990 watts, i.e. 2.9Kw (and by the same math you can see that a 32A socket from your fuse box to a wall charger will get you about 7.36Kw, hence the 7Kw chargers).

But on the home 13A circuit nothing is expected to run continuously. Toasters get turned off after 5 minutes, kettles in a similar time, and even an old 3-bar electric heater has a thermostat that whilst you imagine it's on for hours it's on and off according to the thermostat. Washing machines and dishwashers similarly only engage peak load for short periods of time (if you have a smart meter and put a wash on you'll see this).

In fact the only things in your house likely to actually run a continuous (1hr+) full 13A load are going to be your oven and hob (if electric). And those run on their own circuit all the way back to the fuse box.

Would you put the oven and hob into a standard socket on the plugs circuit? It's extremely unwise to do so, but this is what you're doing with an EV.

So what melts? A modern 13A fuse gets extremely hot, the entire 2.9Kw goes through it and it always gets hot with any load but under constant load that heat never dissipates and over a decent period of time (hours) it really gets hot. Then the plug housing gets hot, in my case I melted the plug such that the half around the fuse had melted into the fuse. Then the plastic safety bits on the pins that go into the socket melted. Then plastic behind the socket facade melted.

I'd got away with home charging about 20 times before melting the plug on the granny lead. But it only needs to do it once to burn the house down and so now I tolerate the PITA that is searching for public chargers.

If you have off-street parking, it's an absolute no-brainer to get a Pod Point 7Kw charger. Consider the cost an insurance policy against burning your house down.

All that said, one thing the sparks said was that if your sockets and plugs were all MK standard ones, that it probably would've been OK or more specifically "You'd be surprised what load they can handle". Those take higher temperatures for longer periods. What you want to avoid are plugs that are too rubberised (and yet that is what is on granny leads and "EV safe" extensions) and sockets that have a less heat resistant back panel (and you probably don't know what's on the back of your sockets, I didn't).