The quote from Stephen Glaister in this Economist piece about cycling in London is absolutely spot on: "There has never been a shortage of bikes in London,” he says. “It’s just that people are afraid to use them." This certainly tallies with the results from that attitudinal survey I wrote about a while back, which found that two thirds of would-be cyclists in London think the roads are too dangerous.
Leaving aside the question of how to do it, making cycling safer would obviously benefit both existing cyclists and those who would be persuaded to take it up as a result. But if they switched from cars it would also tend to benefit pedestrians and other road users (including the remaining drivers), by slightly reducing their risk of being hit by a big heavy motor vehicle at the cost of slightly increasing their risk of being hit by a much lighter bike. And this further improvement in road safety would tend to convince more people to cycle, and so on.
In economic terms, cycling has a positive externality in terms of safety (not to mention health and pollutants, but never mind them for now), while driving has a negative safety externality. As well as that, cycling also causes much less congestion (because bikes are smaller and more nimble), so replacing a car driver with a cyclist is good for other drivers in terms of less congestion.
In a simplified framework where the choice is between cycling or driving, I think this means that there are two very distinct equilibrium states, one with high congestion and a high accident rate in which nearly everyone drives because they are afraid to cycle, and one with low congestion (because bikes use space more efficiently) and a low accident rate in which many more people cycle because it's no longer frightening. Because of the feedback effects involved it would take a lot of effort to move away from each equilibrium, but at some point the system would 'flip' so the feedback effects stop pushing you towards one and start pushing you towards another.
It's at about this point that I should probably include a nice diagram illustrating this all perfectly, but I don't have one so you'll just have to imagine it.
I've tried to find some proper academic research modelling this kind of thing but have drawn a blank. This EU study (pdf) talks about 'traffic category externalities', i.e. changed accident rates in other modes of transport, but is concerned with static quantification of costs rather than dynamic modelling. And this dissertation (big pdf) includes some interesting figures (table 1.3) showing the relative risk that each transport mode poses to others - 96% of the total fatality risk posed by cycling falls on cyclists themselves, as compared to 47% for cars and just 7% for HGVs.
The real world is obviously a good deal more complicated than a simple model like this - for example in London we rely heavily on a bus system which doesn't really involve that kind of driver-based decision-making. But it still seems fairly clear to me that we are in a position where a huge number of would-be cyclists are too frightened to cycle, and if we could improve safety enough to tempt them out it would not just benefit them but the rest of us too.