Hampstead Heath
Not a park so much as a piece of countryside that London built around rather than over. Three hundred and twenty hectares, unfenced and deliberately unmanicured, which is why the paths turn to proper mud by November and why every dog you pass is filthy and delighted about it. The view from Parliament Hill is the one on the postcards.
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.