Public transport will be a viable alternative only where the routes are simple and regularly served and there is no need to carry luggage. Even then the time or cost difference must be considerable to be persuasive. One day's car parking in central London costs about pounds 25 and this is probably the main reason why most (but, significantly, not all) workers take public transport.
Road-pricing or city centre charges will not work unless set at extremely high levels. Improvements in public transport must be equally vast to make any difference. Reducing the price won't work, but, for instance, during the current heat-wave, how many drivers would remain steaming in their cars if all trains, stations and buses were air-conditioned?
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