You right it's an 60A CU. So in the first instance will get that changed to a new/current unit
In that case, it should have been a 60 amp DNO fuse as well. The fuse carrier is likely 100 amp as is mine, but the fuse inside it likely 60 amp, some times there is a sticker to tell you.
The EV has evolved, around 2011 my neighbour got a Renault Kangoo electric van for his milk round, it would only charge at 3 kW, it had a claimed 140 mile range, but he would some times need rescuing due to flat battery and his round was a fixed 68 mile, seem to remember it was 22 kWh battery, which would take about 8 hours to recharge. The battery sizes have since jumped to 33 kWh and then 44 kWh so it has now double the capacity of the old van.
The result is the chargers have also increased in size, and now 7 kW single phase and 22 kW three phase seem to be the standard AC charging units. So your looking at 30 amp for a long time, 4 mm² may be OK for a cooker, when max power is only for a short time, but for an EV charger, 6 mm² when buried in a wall, is more the order of the day, outside where in free air you may get away with 4 mm² but not when buried in a wall.
There does seem to be a problem, it is assumed if one can afford a EV, you can also afford the EV charger, this does not take into account the company car, where the company is concerned about their corporate image, and even if a petrol or diesel would do the job better, they want their staff to use an EV.
I know years ago, I was lucky, both my son and I shared the works van, so neither had to pay extra income tax to take it home, but taking the van home often resulted in paying extra income tax. Not a clue if that is still true? It was a duel edged sword, if you stopped owning your own car, and used the company car for everything, then you could gain, but swap jobs, and you needed a new car fast, having an EV charging point installed to charge a company car, can leave one with a unused charging point so easily. I would not personally want an EV charging point for a car I did not own. But one would want a method to record the power used.
I upgraded my consumer unit, and still I could not have a 100 amp supply without adding an extra fuse. The solar and battery plus the grid do not exceed 100 amp, but that is with a 60 amp DNO fuse, if a 80 amp was fitted, I would exceed the 100 amp total.
With solar an EV can be used as a energy store, not sure how it works, but I know I save a lot of money charging my battery at night at cheap rate, and using it during the day, since most of my trips are short, the EV could even simply standing in the drive, save me money, but even as an electrical engineer not sure how this all works.
So even as an electrical engineer I would not be doing the work myself, it is a specialist job.