From what has been on the news channels lately discussing Londons ULEZ and also Newcastles, once the systems are in place and vehicle registrations and movement can be tracked then to maintain income once vehicles are compliant with emissions then it is a simple process to charge for distance traveled instead. It was also noted these vehicle movement cameras are more widespread across the country than many realise but at the moment only used for highlighting conjestion and bottleknecks but easy enough to log individual vehicle movement.
In many cases people got cars because there was no local employment, in the days of big british industries that had large workforces they laid on buses and many walked / cycled to work, a good example in the seventies was Marconi and RHP in Chelmsford that employed huge numbers of locals, now a dormitory town where many drive to work elsewhere or get a train. Now we have many smaller firms and busineses spread far and wide it requires a more complex transport system but as you say people would use public transport if it was good value and reliable. In rural areas like where I am everything is a mater of miles to get anything and we don't think twice about doing a seventy mile round trip for shopping and wood.