Dulwich Park

Victorian and flat, opened in 1890 on land given by the Dulwich Estate and laid out around a carriage drive that still makes a tidy circuit of about a mile. A boating lake in the middle, and rhododendrons that Queen Mary came to look at every spring. Smaller than its neighbours and better kept than most of them.

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.