How Things May Pan Out
Considering many people (exactly how many in Blighty, I don't know, seeing as I'm on the other side of the world) will have garages/carports where they can comfortably trickle charge, the need for rapid charging won't be as high as the need for petrol stations now, but there would still be some need.
Keep in mind that although street-parking has its limitations, carparks at or near people's work can offer day-time charging, even if the carpark's local Li-titanate (or equivalent) storage is trickle-charged overnight from the grid (this was demonstrated in California in the 1990's). And it's feasible, albeit not ideal, to build street-side charging points in some neighbourhoods (probably limited to trickle-charge, but it can be made safe and weather proof and controlled by electronic meter, similar to electronic-metered parking). I'm sure creative minds will come up with additional solutions. Of course, this assumes that driving range is short enough to require frequent charging ... if, in the long term, driving range is say 1500+ km per charge, then the problem is much reduced.
I expect there will be greater incentives to use public transport offered as part of the mix of solutions. (As much as I'd like the future to be houses, garages and cars, it will, unfortunately, increasingly involve high-density apartments and public transport).
In the medium term, I'd see plug-in hybrids as the preferred private vehicle approach, which defers questions of electrical infrastructure until technology matures and the economics are clearer. In the long term, all-electric seems best. I don't see "a sub-station behind every forecourt" as a problem - there will be fewer forecourts and that situation is many years away yet. And, IMHO, that infrastructure is simpler and more versatile than large-scale hydrogen infrastructure.
I think the future won't be 100% battery-electric, though, as much as I'm a strong advocate for battery-electric(#) on efficiency grounds. There will be niche applications, specialised vehicle types and some personal circumstances that would require something else as an additional energy source, e.g. long-distance haulage, buses, emergency vehicles(##). It may be that, despite the options mentioned above, some private citizens may prefer to still use plug-in hybrids - in that case the additional energy source may no longer be a small petrol/diesel engine - perhaps a hydrogen fuel cell or bio-fuel engine, even though it won't be as efficient or as cheap (by then) as all-electric.
Lewis has correctly pointed out that there are still plenty of problems to work on, but I believe that the need for energy efficiency will drive us toward a predominantly battery-electric transport future.
Perhaps there's one thing we can all agree on now: People's current expectations and lifestyles will not remain fixed - and that's going to be one mighty PR issue for governments.
# Other direct-electrical storage technology could conceivably replace batteries in the long term.
## The military have somewhat different vehicle energy problems that may lead to quite different solutions.