"the vans could charge up during the early morning when there is excess capacity on the grid."
Go look at the power demand curves on Gridwatch. Now realise that if 1/4 of the cars in the UK were EVs and charging overnight, peak demand would be during the early morning hours.
And for London in particular, metling down substations/exploding pavements would start being the norm. The UK isn't that far removed from the events of Terry Gilliam's "Brazil" (where the terrorists never existed, the entire infrastructure was simply falling apart and blaming terrorists was an easy way of pretending it wasn't the government's fault)