Hi, Taking into accoun I have not seen or done any tests on your system, I can only hazard I guess what might be causng the problem.
The O PEN device (if fitted) in your charger, monitors for a rise on the DNO neutral cable and will disconnect the supply if a PEN fault is detected on a PME earthing syetem and removes the need for an external earth rod to be fitted. The O PEN device could be out of tollerance, fauty or it is indeed doing its job as should, detecting a fault.
The current clamp monitors the total load in amps goining through your home and will disconnect the supply if it is reaching close to the rating of your cutou fuse. I doubt it wll be this but, it is possible with the right equipment to measure wether there is a fault on the charging circuit somewhere. CP incorrectly set diode fault.
Faulty charger.
and so on…..
Have you tried charging during the day for a couple of hours to see if the fault replicates itself or have you a neighbour with an EV, who would be willing to charge there vehicle overnight to see if the fault still happens. I would also inform Motability and demand BP send an engineer out to determine the fault!