How many kilowatts?
300 miles is about 90kWh, based on current EV technology. 90kWh in 10 mins means delivering 540kWh in an hour.
That means a 3-phase 400V feed pulling 1350 Amps. It's the equivalent of running 180 3-kW electric fires at a time. Fire one of these up and the lights dim for miles. You'll need a 2-in diameter copper wire to feed it.
Typical UK home uses about 3000 kWh per year. Switch to a car doing 15,000 miles a year, and you add another 4000+ kWh per year to that. Can our present grid infrastructure handle that? Not in a lot of rural Wales it can't. Sub-stations are already close to maxed out. How many billions to upgrade the grid? When? And who pays?
Topping up at a motorway services? Okay, there will be fewer people using them than for petrol at present, as we assume they're all full when they leave home. But they'll probably want to plug straight in to their private pylon, or have a small nuke station in the car park.
This is the elephant! The approach of having everyone use EVs with Li-Ion batteries for long range is not feasible. They're fine for local commuting - max 100 miles a day, charged at home (if you can). But don't try and replicate the current usage pattern.