A 'smart' meter, as we know it, alone could not do that. They can record energy usage during umpteen different time windows but, within any time window, all they can measure is
total energy usage, so they wouldn't know how much of that total was attributable to EV charging - to determine that would need some sort of 'smart chargers' (or an additional meter!) that could measure their own usage and report it to the meter - so you can probably factor in another few more decades for rollout of 'smart chargers' if they go down that route
As you imply, they are presumably going to have to find
some way of recovering the equivalent of the (enormous amount of) fuel excise duty they currently receive. They may try to do it, as you suggest, by taxing the electricity used for charging but I suspect that, as 'smart cars' come along, fuel excise duty and vehicle 'tax' will probably be replaced by a single usage ("per mile") tax/charge - which may, in some senses, be fairer than the present situation.
Kind Regards, John