A few points in this post to think about.To be fair incompetent people have been putting heavy duty 3kw loads onto 13A plug top outlets for many years without too many fires.. houses with spa pools, self-installed electric showers, cookers, dodgy electric heaters and so on .. The 2300w the car charger pulls is actually quite modest and totally manageable by 99% of home's ring mains, as long as they've not been hideously bodged.
Cookers, at least one designed to plug in via BS1363 plugs, have low duty cycles, not 10hours or more.
Plug in electric showers, new one to me.
Electric fires, yes I've had the melted plug. Anything in my and my kids houses have thermoset plugs now. Spa pools, wow careful, risk of electrocution if not installed as per regulations, etc