Finsbury Park

One of London's first public parks, opened in 1869, and named after a district a few miles south of it because that is who the land was bought for. It slopes up gently towards the north, which you only really notice on the way back. Properly urban, properly busy, and about as central as a park this size gets.

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.