I lived in London for the best part of a year and found it to be pretty reasonable for cycling. Bear in mind though that the criteria that I use for determining the friendliness or otherwise of a place has less to do with the nature of the road (how wide, how many lanes, bike lanes/no bike lanes etc.) than it has to do with the courteousness of the other road users, primarily car drivers.

On average, I found drivers in London to be quite friendly and courteous, and I hardly ever felt deliberately threatened, nor were very many drivers overtly aggressive. Black cab drivers were an invaluable resource if I was ever unsure of my direction. This was 7 years ago though. I have no idea what it's like now, although I can't imagine it'd be significantly different.

Despite the greater population, greater population density and bizarre ancient road network, I actually think it's better for cycling there than it is here in Brisbane, simply because of the higher moron quotient we have here.

The pollution, as Poululla pointed out, is a problem. I recommend a breath mask if you're going to spend a lot of time in central London.

Hyde Park, on the other hand, was a bloody menace. It shared the same problems that any shared path has, only moreso due to the extraordinary number of people using it. The only cyclist fatalaty I heard of during my time there happened in Hyde Park - a collision with a rollerblader (the blader was pretty much unscathed IIRC).

Richmond Park makes for a nice place to do relatively unihibited laps in a beautiful landscape, and the Thames tow path down to Surrey makes for a nice easy day out, with plenty of pubs on the way. (this was actually part of my regular commute when I lived there. Sometimes I really miss that place - even the belligerent Canada geese).