Whitely Park, a dog off leash area in Blackheath. Fully fenced, a wading pool and balls often found for your fur friends to play with, a great big stump for them to mark, interesting smells and tracks for them to explore.
you will be out of sight from most while signing the log, the cache is in plain sight but unlikely to be spotted by muggles. You will certainly be less obvious if you have a geodog with you.