I don't think anyone who charges their main vehicle at home would sensibly use a 13A socket.
Most domestic UK supplies are 80A, mainly confined to older rural properties, or 100A. Unless you have some other overnight demand such as electric storage heating, you could very easily tap 30A, or 7.2kW - giving a theoretical 7 hour overnight charge of up to 50kWh, not allowing for losses.
There's no reason why this couldn't be increased to 50A and 84kWh if necessary, or even higher from a 100A supply, whilst still leaving some leeway.