Well it obviously changes from city to city, but in central London there are very few multi-storey car parks, and far fewer people who drive into central London and park there. So which cars do you ban? If you ban all private cars in London, you will find that most of Zone 1 will still be 80% full of motor vehicles. Because most of them are Ubers, club cars, taxis, delivery vans, trade vehicles, lorries, and various other types that are not private owned.
What next? Ban all club cars? Still lots left. Ban all Ubers and private hire vehicles? That's going to be really helpful to millions of people who have to take a journey that for any number of reasons is not viable to do by other methods.
And even after then you still have thousands of van and lorry deliveries of heavier items, and trade repair vehicles that simply cannot be replaced by bicycles, no matter how much some might wish otherwise. So you've taken the yes, extreme measure of banning cars and private hire/ taxis from a massive area, only to find out that there's still plenty of motor traffic around.
So yes. Small pedestrian zones exist already everywhere, including a few in London. But a city-wide private car exclusion would be an extreme meausre simply because it would not solve remove motor traffic from London, only reduce it by a modest percentage. That model might work in some small towns somewhere in the world. Will never work in London, no matter how people stomp their foot pretending otherwise.