The route starts close to Waterloo station & passes through six Royal Parks north of the Thames. The route then crosses south of the Thames & goes through Battersea, Clapham, Dulwich ending with a tour of Crystal Palace Park.
Route description and GPX can be download from https://ldwa.org.uk/London/W/10413/2026.html
You can use the interactive controls to zoom in and out and to move around the map, or click on a marker for more info. (interactive map help)