I've recently been using the Wandle Trail (via my Colliers Wood route) to get to Turnham Green to see my mum. It's a nice route but has a few problems - Earlsfield town centre (the "Wandle Gap") and the Wandsworth Gyratory. (Following river valleys means you avoid South London's hills, which is helpful on a 15 mile journey).
This route ignores the Wandle - heading instead for the Beverley Brook at Wimbledon Common, and following it (roughly) up to Barnes, where it's a short hop to the railway footbridge over the Thames. From there there's a railway path that heads up to Chiswick House Grounds, then it's the A4 underpass and on to Turnham Green.
Have ridden bits of this but not the whole thing. The maps aren't terribly clear on where you can/can't cycle north of the Upper Richmond Road. White Hart Lane is the quickest way but a bit on the busy side - Vine Road and along the railway would be better, but appears to suffer from West London's rather anal attitude towards cycling.
Will be interesting to ride this one and see how it compares to the Wandsworth Common routes.