I should say that here practically speaking "the public" mean public opinion, and public opinion mean the middle classes. The poor did not regard the police as benign:
'As regards the police, the hatred of a costermonger to a "peeler" is intense, and with their opinion of the police, all the more ignorant unite that of the governing power. "Can you wonder at it, sir," said a costermonger to me, "that I hate the police? They drive us about, we must move on, we can't stand here, and we can't pitch there. But if we're cracked up, that is if we're forced to go into the Union (I've known it both at Clerkenwell and the City of London workhouses,) why the parish gives us money to buy a barrow, or a shallow, or to hire them, and leave the house and start for ourselves: and what's the use of that, if the police won't let us sell our goods?—Which is right, the parish or the police?"'
Henry Mayhew, London Labor and the London Poor (http://dl.tufts.edu/catalog/tei/tufts:MS004.002.052.001.0000...)
[edit: added "here" to first sentence.]
