Peckham Rye
Two things at once: a flat open common, and a park of proper gardens behind it that opened in 1894. William Blake was about nine when he looked up here and saw a tree full of angels, which his father nearly beat him for reporting. The common is the dog half, the gardens are the quiet half, and most walks end up doing both.
Hapoo counts the walk you were doing anyway
Read off your phone's motion sensor after the fact, so there is no start button and nothing running in your pocket. Characters turn up at real park gates across London, this one included.