Given your with EDF, why dont you setup a schedule on the Ohme charger to start a 12am and finish at 4.59am or set the charger to charge when plugged in and control the schedule from your car.
What are your rates on EDF?
Your comment yesterday for 6.3kW costing £1.01 amounts to 16p kWh, which is likely cheaper than peak rate but, more expensive than the off peak rate. Remember your in home display will show household useage plus charging usage, to give a running total cost.