I have the tesla charger.
I'm on an E.on tarriff, I don't think they're selling it anymore, but E.on directly communicate with the car to control the charging between 12 and 4AM, so car is set to start midnight every night and e.on turn it off at 4AM, I have to go into the E.on app if I want to charge any other time and "boost" it.
If I was on Octopus I really wouldn't lose any sleep over scheduling, set the car to start at midnight, then on the rare occasion you need to charge more than 40% (I get 10% an hour) dial back the charge you want, i.e. car on 10%, set to 50% night 1, then say 80% night 2.