And here's my route. Could be done anticlockwise or clockwise (this route is shown anticlockwise).
http://ridewithgps.com/routes/9755489
I couldn't make it any flatter. It includes a big chunk of the last night ride to Whitstable. A very early start and clockwise would get all the East London grot out of the way first, and breakfast at the Waterfront. But an early start and counter-clockwise ascends the Downs the easy way, and means that the final bit is in a railway station rich area for easy bailout.
I'm not at all confident, but it's something to aim for.