Around the clock or at least on call, there were the parish constables who came at a few minutes notice to aid the night-watchmen.  Every able-bodied, coherent man in the parish had to serve as a constable for a set term when his time came, although it was possible to pay a fine to avoid the duty.  If someone had to be put in the round-house, a constable would have to check on the offender and confirm the decision of the watch.  Imprisonment in the round-house was literally overnight, but prisoners were usually fed and watered.  

Next up, Justices of the Peace oversaw their district.  Out in the parishes, they would have been familiar with the worst trouble makers and dealt with them accordingly; within London they frequently bought their positions and then traded favours and bribes.  The Justices could choose to turn a blind eye, but they could also try minor offences and dole out whippings, fines, pillories and so forth.  If a case was too grave for them to handle, they would commit the case to trial at the Old Bailey.  

Outside local control, there were thief-takers who operated much like modern private-detectives, on a case-by-case basis.  They took a fee from the victim to track down the perpetrator of a crime and bring them in for punishment.  In many ways, they worked like a modern bounty-hunter, but frequently operated on both sides of the law.  More on famous thief-takers in another post.

In 1749, Henry Fielding was made chief magistrate in Westminster, sitting at the Bow Street Magistrates' Court.  Fielding was a writer and a gentleman, but more importantly he was an Old Etonian and friend of William Pitt the Elder.  He had many other influential friends and between them, they had managed to establish a central, government fund that would pay for a body of men to enforce the consequences of crime.  As incredible as it seems, the idea of a 'policed state' was as feared in the mid 17thC as it is now.  The populace found the idea of a life controlled by central government abhorrent, and were very likely to protest if they felt such a thing were being forced upon them.  Instead, the early 'runners' at the Bow Street Magistrates' Court were tagged as gophers who delivered court summons and picked up those who had defied being bound over.  Outwardly, they were a cross between a barristers clerk and thief-taker.  They worked out of No. 4 Bow Street, but wore no uniform (I know, disappointing for the Robin Redbreast theorists).  They did however, travel across Britain to catch their man, and were very successful.  

By 1754, Henry Fielding's health was failing and he 'gifted' his position to his blind half-brother John Fielding, who could apparently tell a liar from the sound of their voice.  This, I am not entirely sure about, but it cannot be discounted, and John Fielding had no small success during his tenure at Bow Street.  

The Runners tended to be London born and bred; they knew the people, the ghettos, the pubs and brothels where people could be found.  They didn't flinch from serving notices, warrants or summons and they were effective in solving crime.  Although the government support for their activities was covert, it was present and it worked.  In the 19th century, policing would go from strength to strength, and by then John Townsend, one of the early Runners had become 'friendly' with George IIIrd and promenaded with him, telling the King risqué stories.  Townsend was reputed to wear a handkerchief between his head and hat, and he raised the hat any time someone (including himself) mentioned the Royal family: clearly a character.

More on individual Runners, cases and the evolution of the London Metropolitan Police another time.