Sir Robert’s bobbies, who were known formally as “constables,” were no exception. The bobbies were asked to sign each of their blotter entries with name and rank. For patrol officers, they were supposed to sign their name and “Constable on Patrol.” To shorten the last laborious task of reporting one’s actions from the preceding shift, the bobbies shortened “Constable on Patrol” to C.O.P. This is the most commonly accepted origin of the term cop.
A more American version of the origin of COP comes from the New York Police Department, NYPD. Their version of the term cop comes from the copper badge that very early NYPD officers wore to distinguish themselves to the public as police officers. The term “coppers” was still used in 1930’s movies starring the likes of James Cagney and Edward G. Robinson.http://www.annarbor.com/news/crime/cops/