The London Congestion Charge, introduced in 2003 by previous Mayor Ken Livingstone, allowed vehicles to begin moving more quickly again by reducing the quantity on the road, though not by enough to avoid This Is Local London publishing the immortal headline "London cars move no faster than chickens"!
In the first year of its operation, Transport for London estimate over 60,000 journeys by car "evaporated"; moved to public transport, car sharing, and more trips by walking and cycling, against a background of growth in the city, as detailed in Tom Barry's excellent Street Talk on the state of London transport.
A decline in the volume of traffic kilometers travelled in London against a background of a growing city continues even today, as evidenced in the most recent Travel in London report from TfL. Whether it is inside the inner London congestion charging zone or elsewhere, the distances journeyed are decreasing. Traffic speeds during peak hours in inner London continue to hover around 15km/h (about 9.5 miles per hour, or a very gentle bike ride).
Fellow blogger Mark from As Easy As Riding a Bike has all the data that's fit to print on the fluctuations in vehicle speeds and volumes in an excellent blog post here.
And even the motor-headed cast of the BBC's Top Gear have shown that when it comes to a race across town, the bicycle wins.
If less traffic in London means there is more space (and certainly there seems to be enough new space to justify ridiculous carriageway narrowing schemes in the City and in Westminster), then that space could be put to good use getting more people around more quickly.
The "Speed" poster from 1915 is not just a charmingly aesthetic relic from a city of another age. It shows there have always been smarter and faster ways of getting about than by filling the city with traffic. I'm as interested in the economics and efficiencies of cities as I am in cycling and cycle infrastructure, and it seems clear to me that not only is there latent demand for more safe space for cycling, but that it makes very good sense to introduce it: not just for the cyclist, but for the sake of the city itself.
Even if you spent billions burying half the roads in London there will never be enough space to allow many motor vehicles to be driven here at any useful speed. But creating a city that allows people on bikes to move around quickly and safely is an easy goal to win. As London Underground's poster shows, time is of the essence.