Avenue Verte is a cycle route that was created for the London 2012 Olympics. It runs from the London Eye, next to Waterloo, to Notre Dame in Paris. It crosses the Channel on the Newhaven - Dieppe ferry. The French care a lot more, with the route being well signed.
Most of the route in England is part of the NCN network, however from Westminster to Wimbledon, local routes are used, including CSH8. In Central London, NCN4 is used. From Wimbledon to Reigate, NCN20. From Reigate to Crawley the route is a multiplex of NCN20 and NCN21. Avenue Verte takes the latter from Crawley to Polegate, and then NCN2 to Newhaven.