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I don't know if anyone has chimed in yet, but you don't have to go up Page's Walk on the route that you have posted
Just follow Q1 past The Victoria, instead of turning up PW and you can pick the rest of your route up after the (cycle specific) lights without going onto Grange Road and the junction with TBR.
You may even find that if you continue to follow Q1 for its entirety, its a better and safer route.
EDIT - You do follow most of Q1, you just miss out the bit out I mentioned above.
This is my daily route, which cuts out any busy dangerous bits at all, has hardly any traffic lights and uses quiet routes and established cycle routes. It avoids the busy and dangerous route down to Peckham via the main road
https://www.plotaroute.com/route/203824