We're pretty close to a point where it would be practical to do it in central (maybe up to zone 2) London, for example. In fact, it's already the case that "car free" housing developments where you are not given any parking place are commonplace.
How long it will be in other UK cities depends on how quickly politics allows progressive, incremental restrictions to be introduced.
Here's an example of a small city in Germany which did it a quite a few years back.
In Freiburg, Germany, a neighborhood called Vauban made it unnecessary to own a car–and very difficult to do it even if you wanted to. After 20 years of success, it could be a model for how we design future walkable neighborhoods.
www.fastcompany.com