If ou want to permanently reduce road use by motorised vehicles, you will need a huge rethink.
The lockdown (or something very similar to it) will be need to be permanent.
The only way to reduce car use is to reduce travel.
There's not enough capacity to put current car travel onto the railways. Before lockdown, the railway had higher passenger km's ever, even with fewer lines far more people are travelling by train than 100 years ago. As for freight, well I do a lot of work in the rail freight sector and before lockdown getting NEW paths for new freight trains flows could be extremely difficult as the railways are full. (We don't need HS2 so much as a new W10 gauge freight line IMHO, however I digress).
All out of town shopping would have to go. Home deliveries would be difficult without vans (I have both a big van and a cargo bike and I can assure you a big van holds a LOT more stuff), although in densely populated cities the last mile by electric cargo-bike derived vehicle might work OK. Bus riding would probably increase- you'd really need to bring back trolley buses or trams in cities/big towns although it wouldn't take anything like the current levels of car traffic.
Where I live, commuting to nearest town about 10 to 15% is by train. Even doubling that is only 30% and even if you got another 20% by bus that's still another 50% to find- and cycling is unlikely to work where people live 20 to 30 miles away from work (not unusual).
So, life would need to change- a lot.
No more weekend breaks in the country or second homes/caravans- unless you are rich. House prices in cities would need to fall a lot so people can live close to work. Of course we also have a lot more people now than in (say) the 1950's which doesn't help. One family holiday a year if you are well off enough- and it may only be a train to the seaside.
Jobs would need to be close to home and in quite a few families that would be the end of the mother (usually) working as the family would need to live close to work. Of course, no choice of schools- you must attend the nearest school.
This is how things used to be not so long ago- in the 1970's, in all the time I was a child at home we only ever had one family holiday to a chalet in the lake district subsidised by dad's work- we couldn't afford anything else and we were far from "poor." During the times we had a car it was an old banger nursed to life by dad but usually he cycled to work and mam walked to part-time work in a local shop. Saturday we'd get the bus to mam's parents- they had a nice council house with a big garden complete with veg patch and shed and granda supplemented grub by catching rabbits at work as a night watchman.
Mam made our clothes and food was NOT to be wasted. If the bread got dry towards the end of the week you just ate it dry.
What I am getting at is that our current (high) standard of life is all supported on having a lot of road transport- cars, vans and HGVs.
Only people who live in London (or it's environs/key catchments) have decent public transport BTW.
Personally, I'd much rather swap my work away (where I sleep/live in my van overnight) for something local, in fact I used to work locally until I was made redundant, set up a business and found customers- just not nearby. But as I work from home at least 50% of time and travel to a place then stay there in the depot car-park for a week, travel is minimised. I wonder how many people would work away like that though, when I was a bairn it was not unusual for us Geordies to do that seeking work in the south but it's not exactly a favoured way of earning a living these days. Although of late there is a trend of skilled contractors staying away in a caravan/van as hotels get costly as they cater to the weekend city break and student market......
I wonder how many people you could persuade to vote for such whole-sale change? Returning to a 1970's level wouldn't bother me, but it would bother a LOT of people for whom weekend breaks, shopping out of town being a leisure pursuit and eating out at drive-thru places are a BIG part of how they have been living until lockdown.
But in real life, that's what it would take to ban the car.
GC