There is no sensible advice one can give about this other than to adjust one's speed to the conditions. At times, in town, that can mean travelling as fast as the fairly slow-moving traffic, because that is the way to take the lane and ensure both visibility and freedom to manoeuvre. But certainly it makes sense to moderate one's speed in many urban situations. I see a lot of commuters cycling as if they were time-trialling and taking far too many risks - both with their own safety, and that of pedestrians - as a result.

But I wouldn't agree that it is obvious most accidents happen at relatively high speed. I believe the statistics show that most accidents to cyclists occur at junctions, and in some such cases the cyclist will be just moving away having been stationary. Being aware of the vehicles around you, and how to minimize the risks they pose to you, are the critical factors here.