I'm of the slightly warped mindset that enjoys the bump and grind of central London traffic. You can't do it absent-mindedly admittedly, but traffic speeds are relatively low and you learn to be looking ahead and assume that if it can happen, it probably will, and take the appropriate evasive action. I clamber up Crystal Palace hill, swoop down through Dulwich, Camberwell, Elephant and then over Southwark Bridge and it's quite an enjoyable ride, usually good enough for me to make an excuse to the go to the office if the weather is sunny.
Of course, if I turn up at the meeting and anyone notices that I've cycled, there's the usual discussion about "isn't it dangerous?" and the standard incredulity. I suspect some people think that cycling into London for a meeting is akin to navigating up the Congo in a pedalo.