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You're going to end up crossing a lot of the High Weald which is not flat. I reckon you could probably net out at just over 2000m climbing if you finesse the route a bit.
That'll probably send you down more busier roads though, to miss the sharper elevation of the smaller lanes. So there's a balance to be struck, as they're less fun especially if you're less experienced.
honk
I'm trying to route the flattest 200k I can from SE London down to Eastbourne and back, so thought I'd check here for inspiration. The only chat I could find was @hippy trying to build the lumpiest version possible, whereas I need to do the opposite. I'll be riding with a group of mixed ability and worry anything much more than 2000m total climbing could end up being a loooooong day and not much fun for some. Is it doable?