I think the National Grid will need dynamic load controls - to increase or decrease consumption automatically to balance generation.
Won't smart meters be sufficient? i.e. divert excess into car batteries whenever there is excess? Off Peak is fine too of course. 90% of my EV charging could happily be done 1AM to 6AM, the other 10% is, currently, consumed day time because of need to charge mid-trip on a couple of days a month. But a slightly bigger battery and that would change to once-a-year, maybe less, and then 99.
nnn% of my charging would be off peak. (If I come home empty tonight, and therefore fail to get to 100% (at 7kW) by 6AM tomorrow, I almost certainly don't need mega-range two days in a row, so getting back up to 100% the following night(s) is usually fine)
Possibly small 3 cylinder plugin hybrids are a good transition, allowing say 10 years for the UK to switch from oil to electric.
I'd be very happy with range-extender generators in cars, so they could have smaller batteries (i.e. that are sufficient for 100% of 90% of the journeys). Right now I (unreasonably/selfishly, i think) have a huge battery that I lug about on all trips, and am depriving one or two other cars of having any - whilst industry is battery-constrained.