There’s a thread elsewhere on it. It would need some fairly big investment in the electricity distribution network in some places. But almost certainly not as big as the investment required in the public transport network to electricify and expand that.
There is a good deal of spare capacity in the U.K. generation network at night (around 20-30GW) which is precisely the time that most road vehicle owners would charge their vehicles. There’s also a fair amount of renewables under construction, mostly wind farms, with more consented to nearly double wind power capacity in this country (to well over 30GW). Obviously that needs the wind to blow (it usually is, somewhere in these isles), but also has the problem that on a windy night there will be too much power generated compared to current demand, and it needs somewhere to go. Ideally this would be a widely distributed network of small scale energy storage to ease the strain on the distribution network. Like, for example, a lot of batteries.
That’s not to say that public transport will be abandoned, far from it, but the social economics of some lightly used lines will become particularly interesting.
The consequences of the electrification of road transport are far reaching, not least on taxation, but rest assured it is happening, and indeed accelerating.
