Its highly likely your cut-out is 80A, especially as yours has a stcker on saying so. 80A is sufficient to run a charger and your house in most cases, plus a CT clamp will be installed at the time your charger is.
I would leave Ohme or whoever they use, to notify the relevant bodies after “you” have done the survey they request.
The CU will sit adjacant to your meter box. Have a look on the Kerbocharge thread where @Phaedra shows where the CU sits next to the box
What rating MCB’s do you have in your house consumer unit and I’ll check you maximum demand.