With Octopus you can go to an Agile tariff, where you're paying exactly what the market rate is, which means that frequently at night you are being paid for using electricity(the rate per kWh goes into negative). I know a few people who have it with an electric car, and it means that at certain times you are being paid to charge your car. It's crazy. But also it means that at peak times the cost can be as high as 25-30p/kWh
There are apps that can automate this whole process for you, monitoring the charge your cars needs each night and the dynamic energy prices either on an Economy 7 or Agile tariff and then controls the charging to optimise the price. If you're car needs less charge than your off peak rate time period then it will charge at the lowest carbon times. https://ev.energy