Many different cities are trying various schemes, and they watch each other to see which ideas seem to work better than others. I grew up near Los Angeles and went into the "downtown" section on occasion. I saw the congestion get worse every year, then I resolved to never go again. Once I was required to and rode the bus, but although someone else drove the bus and I didn't need to park, riding a bus that stops at every corner was its own flavor of nightmare.
The federal government can't legally force the states to do certain things, but they can bribe them with tax money. Once a traffic proposal is passed by 51%, we are all taxed in our paychecks, but each state gets no federal matching funds unless thay add some state tax money and then do as they are told. We are federally taxed, but then you must "use it or lose it", so from the list of acceptable projects, LA chose to build a light rail system. Its electric like NYC's subway, but above ground as they have earthquakes there.
Its shaped like an octopus, with the downtown being the center. After it was completed, I had to go downtown again, and tried the light rail. I was pleasantly suprised. It worked well, and prices were kept affordable. Traffic around the center was much lighter as a result. But I noticed one flaw...
The main Los Angeles airport (LAX) in the southwest, had long ago built outlying car parks with bus service to the terminal. To park near the terminal became hugely expensive, enticing most to use the car-park/bus, which brought in significant and steady "revenue". They could have had the light rail end at the terminal, but they had it end at the car-park, so riders had to also pay for a bus to get to the airport. I'm certain the car-park operator was a "friend" of LA politicians...
Once while working in New Jersey (just south of NYC) I rode the train into NYC. Parking a car in NYC is enormously expensive, but the train and subway system is affordable works quite well. As a result traffic is very mild. Those who can afford to insulate themselves from the sweaty unwashed peasants ride in Taxi's or limo's. Every weekend, quite a few people parked in New Jersey and rode the train in for the day (spending their money) but if you raise the rates, people stay home or spend their money elsewhere.
I'm not suprised London is embracing high parking fees, but I am suprised that they are doing it before they install a comprehensive system of outlying car parks. Perhaps with the new costs of driving in and parking, citizens will finally vote to approve such transport projects?