somebody mentioned it was the job of enviromental officers. I heard though that the police were called to a fella who refused to stop smoking in a bar and the coppers booked him for drunk and disorderly instead, fined him and banged him up for the night.
It is environmental officers who dish out the fines for individuals and premises. As the smoking ban is law, the police are obviously involved in enforcing that law when all other means have been tried and tested.
Because its a civil law I think persistent flouting of the smoking ban can lead to a court appearance with heavier fines.