We can extract all the Lithium we need from ground water, especially in the UK where there's more than enough. Yes, uncontrolled mining causes enormous environmental damage, but so does oil extraction, so it's not like we'd be making the environment significantly worse off by switching.
Projections based on current levels of car ownership, especially in cities, often fail to take into account that individual private cars in urban environments are expected to become the exception rather than the rule.
People in cities like London don't generally need to use a car every day as there are adequate public transport solutions available, but even if you take the national average commuting mileage of 2,700 miles per year for the 2.5 million cars in London at 4miles per KWh that indicates a need for 675KWh/car/year in charging capacity. Spread that out over say 300 days a year and you get a total demand of 5MWh per night or 1.5GWh/year
This would be spread over the 3.8m domestic meters in London, each of which consume around 3MWh/year. So you're talking about increasing a total consumption of c. 11TWh/year by another 1.5GWh, an increase of around .01% in total energy demand. With decreases in car ownership, increases in home/flexible working, and V2G technology this seems entirely plausible that we can cope. If there were to be anyone shouting about the issue you think it would be the National Grid company and the DNOs but they are happily cracking on with the job.
Sure, there is currently a lack of charging infrastructure, but banging in upgraded cables and figuring out some time-sharing apps to synchronise charging loads is already underway. Our local DNO is putting in upgraded cabling all over the place, sometimes is seems that every road around Stroud has got Western Power contractors working on it.