Greenwich Park

Steep, which is the thing nobody mentions. The climb from the Maritime Museum up to the Observatory is a real climb, and what is waiting at the top is the best view of the city from the south side of the river. The deer are fenced into The Wilderness, so the hill is the only thing to plan around.

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.