I believe that you can be safer as a cyclist in London if you are also a car driver. When you drive you quickly get a sense of when cyclists appear to "pop up" from nowhere. This is useful information when you are then on a bike.
The other thing - you get a good sense of which side of the road to drive on. Quite often, on the Regent's Canal on my way to work, I'm surprised to find that fellow cyclists don't seem to be riding on the left. I put this down to the fact that they don't want to fall into the canal, so ride as far away from it as possible.
But another explanation might be that people really aren't used to roads, and road signs. A couple of days ago I went past this bit of cycle lane near Tavistock Square in London. I was amazed by how many cyclists did not attempt to follow the directions:
To me, this means: "OK guys, you now have to go over to the right, to the other side of the raised bit of concrete. Oh and by the way, the cyclists coming from the other direction have to give way to you so don't worry, they'll stop..." In fact, that's not how most people read it - certainly the bit about "don't worry they'll stop". So I guess I'm wrong. Or, perhaps, it's just a really confusing bit of signage.
Sorry, I'm beginning to sound a bit ranty. I'll be quiet now.