The charging rate will also depend on the temperature of the battery pack when it starts. Plus, it may require some battery heating if it is quite cold and a slow start to charging. Or, it may require some cooling before any useful charging can occur.
In the USA, the circuit for a device that can be on for more than 3-hours at a time is required to be able to provide 125% of the draw, which, depending on how you look at it, is 80% of the circuit's capacity.
In my home, my incoming voltage is often in the 248vac range, which is enough to max out my i3 with a 30A EVSE. At least in the USA, a 13A circuit should not be loaded to provide more than 13*0.8=10.4A. If the device is rated for 13A, then the circuit should be 13*1.25=16.25A (an uncommon breaker or fuse rating).
The EVSE itself will use some power, but generally, not a whole lot. It has an internal power supply and a logic board, indicator lights, plus, often a relay coil that will consume some power even in standby when plugged in. Mine only seems to draw about 4-5W, so in the scheme of things, not relevant, but real.