The reason I said non-public transit is high-speed trains do the trip in about 4:30 and planes do it in under 2 hours according to Google Maps.
The distance between either Glasgow or Edinburgh and London is, and will remain, well out of range for electric vehicles, necessitating at least 1 (and probably more) lengthy recharging stops. It is, however, within range of virtually every gasoline/diesel-powered vehicle, meaning there would be no fuel stops during what Google Maps says is a 7-8 hour drive (depending on traffic).
I could have said Milwaukee-to-Duluth because it's the same distance (and something I've done in less than 6 hours), but there isn't (currently) any appetite to kill the internal combustion engine in the US.