All excellent points. (My house is 27 years old and its cut-out fuses are annoyingly hair-trigger. Any time a light-bulb pops, that entire circuit trips. Plug in a faulty appliance, and the same thing happens.)
Annoying of course, but a good indication that the system is doing its job right !.
I am going to make a pure guess that your main cut out fuse will be rated at 60 Amps ?.
Not the one in the C.U. ( fuse box) the one on the main supply cable before your meters.
It will sealed in place with a wire and crimped with a lead tag seal.
It belongs to your local DNO network supplier and should NOT be touched, other than by them !.
I used a Granny to charge our 2015 VW PHEV for about seven months, before having a wall box installed.
How did I find it ?.
It worked just fine of course, but after good few hours of charging, the back of the three pin plug did get warm.
Not stupid hot, but there was heat present for sure.
The socket I used to charge from, was on its own dedicated circuit.
I used this Granny to gain a charge when we travelled away for a short holiday, with the same affect at three different addresses.
Heat was present at the plug top.
When the wall box was finally installed, I retired the Granny lead to the wall of our garage.
Another thing worth considering is this, now you have a full EV if this is your only mode of transport and your single point of charging is your Granny lead, what happens if that unit fails for some reason ???.
Are you close to a public charger by any chance ?.
Owning an EV tends to puts you in the state of mind of :- “Do I have a back up / fall back plan”.
Many EV owners tend to carry a 12 volt battery booster packs for example ( I do ).
I also carry a public type 2 charging cable, plus a spare wheel, and a 10mm spanner ?.