I'm on the Octopus Intelligent EV tariff which varies the tariff overnight. The Octopus app controls the car charging, you tell the app what % you want to charge to and then what time you want it to be ready for and then it decides the charging schedule overnight.
0530-23:30 = 39.25p/kWh
23:30-0530 = 7.5p/kWh
The day rate is higher obviously but I never charge the car during the day and our daily home usage is otherwise irrelevant compared to the car. With the app you can however get peak charging priced at the off-peak rate if demand allows for it, the app does it all for you.
Model 3 RWD is 55kWh usable battery so 0-100% is 55 x 7.5p = £4.13 max, nobody charges from 0% so it's always far less.
As for public chargers most decent chargers will have off-peak rates too, the Tesla superchargers definitely do now.