"These have gone up now in various places in the Ramble [and I assume in other woodlands]. Hope Prospect Park is doing the same."
No, they haven't gone up in Prospect Park. This is the Department of Parks and Recreations answer to the problem? How about patrolling the parks and giving out summonses! I predict that, as in the past, those signs (and any like them) will be torn down by dog owners very soon.
Remember this photo? This dog's owner regularly allowed her dog to hop the fence and run around in the flower beds:
