Figures I've seen indicate that 95% of EV charging is done at night when the grid is relatively quiet and can probably run on renewables.
http://www.telegraph.co.uk/news/2017/07/25/new-diesel-petrol-cars-banned-uk-roads-2040-government-unveils/The grid is probably only quiet between 12 midnight and 5 am - most electric vehicles need a longer charge time than that.
Solar power does not work at night, and in winter in UK we have a lot of night and not much day, we also have a lot of clouds in UK which reduce output of solar. I drive past a lot of wind farms and often see most or all of the generators not rotating, wind often drops at night when the driver of wind ie. mainly the difference in temperature between land and sea, tend to equalise out. The truth is we no longer have a steady, reliable source of electrical energy once we go away from coal, gas and nuclear. Our energy planners live on a different planet to us mere mortals, a place where the sun shines 24/7 and the wind is always blowing in the 'goldilocks zone' of 20 to 40 mph where wind power is viable.
Storing gigawatts of power in batteries is gonna need an awful lot of batteries and infrastructure, and we all know that a charged battery is like a bomb, put too many in one place and you have another potential Chernobyl.
electric vehicles - the inconvenient truth video https://www.youtube.com/watch?v=k6GeHnMwl1c at about 11 minutes in even the CEO of Panasonic batteries (who make batteries for Tesla) says Elon Musk is wasting his time trying to store large amounts of energy using batteries.
Oh, and has anyone noticed that when electricity is used in a vehicle the makers don't classify it as a fuel, because apparently some vehicles can go many miles without using any fuel.
I would have more faith in a government that scrapped the HS2 white elephant vanity project that is out of date even before they start building it and spent the money on new nuclear power stations.