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I've cycled it before when working out that way it's better to go slightly north and go along Greenwich and Deptford Bridge way or even the other one Hornfair and sun in the sands(maybe bias it's my favourite roundabout) but Old Dover then Langton way and Vanbrugh Park can get you around into Greenwich Park avoiding it then go via tunnel and up to join the far east parts of CS3.
Clockwise
This straight line route, how nasty is it?