Running red lights and almost hitting someone is really really bad, but at the same time, pedestrians don't always have the right of way. In London everyone needs to cooperate because there's a ton of people and not much space.

The closest I ever came to hitting somebody was a middle aged man who full on stepped out into the center divider nowhere near a crosswalk without even looking right while I was bearing down on him with a string of motorcycles behind me. I had one car length to stop, endo'ed up and sort of jumped off to the side of him which I could do because I'm on a mountain bike with great brakes and I ride defensively like you say. If I hadn't been there holding the pace, those motorcycles behind me could have been going and lot faster, and frankly they would have done a lot more damage had they actually hit him. I often wonder how people get hit by buses, but cycle commuting in London has shown me: given enough people someone is guaranteed do something ridiculously stupid and suicidal.

Oh and don't get me started about the tourists at Piccadilly Circus / Trafalgar Square (they won't get hit because everyone who drives there knows the herds of pedestrians aren't paying the least bit of attention to what's going on around them).