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Yup - if you don't mind riding up to Peckham, then you can cut through the "surrey canal" path (there is no canal), then Burgess park. Back roads to and past Elephant & Castle and then up to Waterloo. That gives you c. 40% of the ride off road, but on tarmac'd paths. Also Rocket Van Hire on Brandon St do a nice coffee.
Like this: https://ridewithgps.com/routes/13384414
Also, if you want to cut out Waterloo at the end you can cut through to Webber St and pop out by The Cut.
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Ride earlier and get a coffee?
CycleStreets.net suggest nice calm (and windy) routes if you want it quiet, like this one. -
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
Dear commuters, me and the girlfriend are having to ride our bikes with loaded panniers from New Cross to Waterloo next Tuesday morning during rush hour. I'm wise enough to avoid E&C obviously, but would anyone suggest a better route than straight up the OKR, under the fly-over to Borough and straight on? I think I'm big and ugly enough to cope with most things but she's a little timid around lorries.