From the Wikipedia page [1]

Waterlink Way is a long distance cyclepath route in London. It extends from Cator Park in New Beckenham to the Cutty Sark ship in Greenwich, a total of seven miles.

The Waterlink Way is an established part of the National Cycle Network (Route 21). It connects a number of parks and green spaces in South East London while following the Pool and Ravensbourne Rivers. The route was designed to be accessible, with a large number of railway stations including Kent House, Lower Sydenham, Ladywell, Lewisham and Greenwich en route.

In Cator Park, the cyclepath links with the Capital Ring and Green Chain Walk long distance footpaths.

The London Borough of Lewisham webpage is [2].