Alexandra Park
A hill with a palace on top of it, which burned down sixteen days after opening in 1873 and was rebuilt inside two years. The BBC made the world's first regular high-definition television broadcasts from the mast up there in 1936. The park below is bigger than most people expect, and the view south over the whole city is the reason to do the climb.
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.