Aha, one I can answer with ease!
Yes is the short answer - but of course nothing is that simple. I will give you the answer most people tend to agree with...
Cycling is very doable in LDN but only if you are confident. If you are not a confident rider then just start n quieter roads and go from there.
If you aren't confident all is not lost, there are of course some brilliant parks you can go through, but you clearly won't do your entire commute in a park. I'd say on my commute (Clapham to Notting Hill) - 50% of my ride is through parks, the other 50% is a mix of small/side roads and a few larger roads.
As a cyclist you of course get access to bus lanes too so general traffic isn't much of an issue. Just don't make stupid decisions like jumping reds etc. The A4 is the only road I know of that I don't want to be on.
I have lived here for over 4 years and I'd say I've given drivers the finger about 15 times in all, I have had 1 minor incident, where the taxi (go figure) changed lanes without indicating and I was filtering. It clipped my elbow, I didn't even come off my bike.