There was a burst of news stories in the UK about how EVs would melt the grid, you wouldn't even be able to boil your kettle and change your EV at the same time.
The company running the grid had to put out a "myth-buster" PDF to clean up after the misinformation:
Edit: see recent HN https://news.ycombinator.com/item?id=15217697 ; if my moving the decimal point is correct that's £0.06 per kWh.
Overall energy consumption is quite flat: http://ec.europa.eu/eurostat/statistics-explained/index.php/... possibly due to all those EU-imposed energy efficiency directives.