I think Wandsworth Council need to send their dog sign writer back to sign writing college. Not only is this sign grammatically incorrect, it is mising a key word and the punctuation could be improved upon. It really should read...
Dogs, please keep out of this open space.
Another point to note is dogs can't read. Here is a sign I have created that would make much more sense to a dog if the council wanted to keep their open spaces free of canine interlopers.