All the comments about the grid not having enough capacity and needing massive enlargement are just plain wrong -- the grid (and the generation behind it) has spare capacity almost all the time except at short power peaks, because if it didn't we'd get blackouts and power cuts all the time.
Don't just guess based on "if", do the calculations.
The UK grid has a generating capacity, flat out, of ~ 96GW so with 8760 hours in a year it could manage 840TWh if everything ran flat-out 24/7. Annual consumption is around 360TWh, so about 41% of that.
The energy consumed by road transport is around 270TWh for cars, and an additional 150TWh for road haulage, so 470TWh in total. That'smore than current electricity use, and the total is almost exactly the absolute maximum grid generation capacity.
There's no way the grid can run at 100% capacity 24/7, not least because demand isn't constant, nor is supply from things like solar and wind. Even without car charging the peak load can reach ~65GW. There is not "massive spare capacity".
You're also ignoring the simple practicalities of charging. A tank of petrol or diesel holds a lot of energy. No matter what the battery technology is, putting that much energy into a battery in an acceptable time requires levels of current/voltage that are impractical in a domestic situation, and dangerous to handle without training (much more so than filing a tank with petrol).
Yes, we need a replacement for fossil-fuelled ICE vehicles, but we need one that is more practical than batteries.