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From New Cross, definitely give Q1 a go as @amey suggested - https://tfl.gov.uk/cdn/static/cms/documents/q1-waterloo-greenwich-map.pdf
Maze Hill, Woolwich Ferry, Tower Bridge makes an unusual loop with lots to see.
Forest Hill has lots of hills for a quick (>1h) workout. Up to 18%.
inappropriate_bike
I'm located in New Cross! I'll definitely check out some routes to said pub. I'm already aware that the Kent countryside is a very good place to go for road riding on my side of London so I do want to get myself out there!
I ordinarily use city mapper with the 'personal' cycle preference switched on and this seems to already be far more sensible than google's route planner for cycling!
Thank you! And a huge thank you to everyone too for sharing your knowledge on the topic with me so I can begin to settle into city riding as opposed to riding round a suburban little town.