Theo wrote:

You can work out average energy per day, but not how bursty the charging is,
which is what sets the network current.

DECC produces annual energy flow charts, all of transport consumed 57
MToE in 2019

https://www.gov.uk/government/collections/energy-flow-charts

Clearly a tiny amount of transport is already electric (trains, cars)
and a huge chunk of it would be "challenging" to convert to electric
(planes, ships, even lorries) but just run with the number and that's
660,000,000,000 kilowatt hours

In terms of 7kW charging points, it would need 55 million of the things
running 24x7, then you need to worry about fossil-electric conversion
losses, grid losses and what to do when it's dark or not windy ...