From the longer Wikipedia page [1]
The South East London Green Chain, also known as the Green Chain Walk is a linked system of open spaces between the River Thames and Crystal Palace Park in London. In 1977 four London Boroughs and the Greater London Council created this Green Chain of 300 open spaces to protect them from building activity. The four London boroughs are Bexley, Bromley, Lewisham and Greenwich. Many parts of the system are also part of the Capital Ring route.
The system begins at three places on the River Thames: Thames Barrier, Thamesmead, and the riverside at Erith. There are various circular walks along the route, and there is an offshoot from the main route to Chislehurst; and the final section reaches Crystal Palace via Bromley.
The TfL website is [2]: more information here and here.
See also Capital Ring