A standard European 400 kV power line can transmit more than 1 GW over hundreds of kilometers. Upgrading the grid will not be cheap, but the required technology has been well established for over a century.
"An academic study suggested the e-highway system covering all but the most remote parts of the UK could be completed by 2030 at a cost of £19 billion (£26.4 bn),"
In context that's about the same cost as Crossrail.
Interesting, if that becomes a thing then a lot of trucks could arguably do with a lot less batteries and thus waste less power lugging them around. Sounds like a win-win.