Agree entirely. After cycling in London for 25 years, I've recently discovered cyclestreets (http://www.cyclestreets.net/). It has transformed my cycling experience. The advantages of side streets are - (1) Lower speeds, either by humps or just the topography, so if you do have a collision, the damage will be less, (2) fewer, if any, HGVs or buses (3) As Han says, you can cycle down the middle of the road, traffic permitting. You can see anyone coming ahead and (if you have a mirror) behind you, in good time. (4) Less busy streets means you have the chance to take in the sights and sound of what's around you (4) you get to know all sorts of hidden bits of London.Yes Waterloo Bridge, the view is glorious and different every time.
I love my cycle commute, it keeps me sane. I have discovered a route on Bike Hub, the mobile app that uses the Cyclestreets mapping system. It means I am going along quiet side streets pretty much all the way from Brixton Hill to Euston (except Waterloo Bridge).
The Bike Hub app has revolutionised my journey planning in London. I pretty much always choose the quiet routes and thus my cycling has been transformed from being a risky but exhilarating stop-start weaving in and out ride, to a nice chilled amble.
The great thing about the sidestreets = no traffic lights, no inexperienced cyclists wobbling along the superhighways......
You do have to take the trouble to learn a new route - a list of right and left turns clipped to your handlebars suffices. Cyclestreets gives you three optional routes - fast, quiet and intermediate - but there's generally only minutes difference between them on most London journies. The intermediate and quite routes are generally good at avoiding unnecessary hills too. You do need to be more wary of opening doors, pedestrians and vehicles coming out of junctions on side-streets, especially at night, but it's a small price to pay.
Well worth a look