Yep, mass adoption of EVs will increase demand on the electricity grid, and governments - if they're serious about moving to EVs - understand this and are putting things in place. The UK should be in a reasonable position: peak electricity demand was back in 2002, since when the peak demand has actually fallen c.16% - due to energy-saving initiatives (e.g. banning the old types of bulbs and cutting consumption of lighting in most homes by 90%+ at a stroke, etc). It's thought that if everyone swapped to EVs then peak demand in the country would only rise by c.10%, so we're relatively secure in that regard. The reason it's only 10% is because the vast majority of charging would be overnight, which is when demand is otherwise at its lowest.Edit: If EVs get between 2 and 4 miles per kWh charge, that 40 miles is between 10 and 20 kWhs. The average US household uses 30 kWh daily (another number I can't quite wrap my head around--our home averages between 4 and 6 daily, so what the fuck are people doing to use 30 a day?), so that's increasing that electrical consumption by 33 to 66 percent. Last I checked, 60 percent of our electricity is still coming from fossil fuel sources.
We have also weaned ourselves off fossil fuels to a big extent, with only 24% of production currently from that (all natural gas, with zero coal). And we have significant renewables and nuclear production, so have capacity there for increase in the overnight production, and are building new wind-farms all the time.