Brockwell Park

A hill in Herne Hill with a Georgian house on top of it, opened to the public in 1892. The climb is short and what is at the top is the whole City skyline, which is the best argument for doing it. A lido at the bottom, a walled garden halfway up, and a cafe in the house.

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.