There are plenty of tariffs that offer cheaper home charging than that. I get 6 hours of 7.5p/kWh. On a 7kW charger that's enough for a 0-80% charge every night.
I would be happy to be proven wrong, I'd love to switch plans right now.
There's also Agile Octopus if you just want cheap off-rate. You might need to sign up to Agile then switch to Intelligent if you can't do Intelligent directly.
Both require a working smart meter.
You'll need to call Octopus in order to switch, their online signups have been suspended (like everyone else). My referral ID is fresh-cub-249 if they'll accept it over the phone, gets us both £50 credit.
Forget the car -- topping up a 20kWh battery for £1.50 a day sounds like a great deal for people paying 34p per unit at the moment, would save £150 a month.
Where do you get that deal?