This would make sense for situations where the main risk was the driver/operator of the machine, but when it comes to cycling on the road (especially in crazy Central London traffic) I would expect the risk to primarily come from cars.
For which there is some evidence [1] that you are less likely to be involved in an accident doe to external causes when not wearing a helmet than when wearing one - in essence the same effect that helmet wearing has on the cyclist (taking greater risks) it also has on drivers passing cyclists.