Second, how else are cities meant to do this? The fundamental problem is that there is a huge and rising level of driving demand[1], and limited supply. There is a scarcity of road space in London and you can't really add more. Basic economics tells you that you can manage that scarcity through some combination of prices, queues, and lotteries. Throughout most of the 20th century, we defaulted to queues, in the form of traffic jams. You can use the road at zero cost, but you'll have to wait a long time. But that became increasingly untenable as car ownership rose -- the number of cars in Britain has doubled over the last few decades. And traffic jams are themselves unpleasant: they're noisy, ugly, emit pollution, etc. So now cities are using prices too, in the form of congestion charges, taxes, and so on. That's not some punitive "stick" done for its own sake, it's just a tool used to cope with an inescapable economic reality. When you have more cars and the same amount of road, you need to deter an increasing fraction of those cars from using those roads. The "carrot" is providing alternate, more space-efficient ways to get around: bike infrastructure, public transport.
[1] "driving demand" is itself a weaselly, meaningless phrase, because "demand" only makes sense in reference to a specific price level. motorists have been conditioned by a century of car-friendly policy to expect to drive and park for free, but there's no real justification for that. just because the roads are publicly owned doesn't give them the right to use them for free, any more than state-owned railways should have free fares.