The Safe London Cycling map includes this route as a shared pedestrian route

https://www.google.com/maps/d/u/0/viewer?hl=en&mid=1XlpvN9R-Wg7qZHyezO8y-eVlftr4e0WX&ll=51.516975804561284%2C-0.21828576419061996&z=10

The map is linked from TfL blog post from 2021

https://londonblog.tfl.gov.uk/2021/07/27/london-cycle-routes/