Wimbledon Common

Not landscaped, and never has been. Eleven hundred acres of heath, scrub and woodland saved from development by an Act of Parliament in 1871 and run ever since by conservators rather than a council. There is a windmill in the middle of it, a great many horses, and enough unmarked path to get thoroughly lost on, which is either the appeal or the problem depending on the dog.

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.