why are the police referred to as the bill?

Answer 1

In Europe and Australia, in particular, the police do not carry guns but billyclubs.
There is a fmaous British TV show called "The Bill:" a show about the police who walk a beat and help people.

Answer 2

the term "old bill" was the name of a popular cartoon character in the early 20th century which the metropolitan police used as part of a recruitment campaign in 1917. so the name has stuck.

Answer 3

Sir Robert Peel - Home Secretary and founder of the Metropolitan Police. As Home Secretary in 1822 he set up a select committee to consider the state of the existing police offices, watchmen, constables and Bow Street Patrols, and began to contemplate some form of centralisation.

By 1826 he was outlining a plan for six police districts to cover a 16 km (10 mile) radius from St Paul's, excluding the City of London. In 1828 (with a Prime Minister sympathetic to the idea of a disciplined quasi-military police force in London) he began drafting the Metropolitan Police Bill of 1829. He appointed Col. Charles Rowan and Richard Mayne to establish the force as much as they saw fit. On 20 July he approved the establishment of a force of 895 constables, 88 sergeants, 20 inspectors and 8 superintendents.

Sir Richard Mayne, Joint Commissioner Peel stressed that the principal duty of the police was to be crime prevention (rather than detection.) The nicknames 'Peelers' and 'Bobbies' were uncomplimentary results of his decision to make the force directly responsible to himself in the Home Office.

the origins of "The Old Bill" or "The Bill" as slang names for the police. The simple answer is that no one really knows for sure. Over the years at least 13 different possibilities have been proposed, as follows:

"Old Bill" was King William IV, whose constables were an early form of police. (It is often said erroneously that he was on the throne when the police were founded. Actually he did not succeed George IV until 1830)
The play "The Custom of the Country" written by John Fletcher in 1619 has constables of the watch refer to themselves as 'us peacemakers and all our bill of authority'.
Constables of the watch were sometimes nicknamed for the bills, or billhooks they carried as weapons.
Kaiser Wilhelm I of Prussia visited England around the time in 1864 when the police uniform changed from top hat and swallowtail coat to helmet and tunic. Such 'Prussian militarism' may have led to the police being nicknamed after the first (and today less remembered) Kaiser Bill.
The 'old bill' was, in Victorian times, a bill presumed to be presented by the police for a bribe to persuade them to turn a blind eye to some nefarious activity.
New laws for the police to enforce all come from bills passed through Parliament
"Old Bill" might refer to Bill Bailey of the music hall song 'Won't You Come Home...?' used in conjunction with a pun on the Central Criminal Court at the Old Bailey.
In the 1860s there was a Sergeant Bill Smith in Limehouse. He was a popular character and people used to ask after 'Old Bill'.
Many police officers wore authoritarian-looking "Old Bill" moustaches like that adorning a famous W.W.1 cartoon character 'the wily old soldier in the trenches' by Bruce Bairnsfather.
In 1917 the government used Bairnsfather's character in posters and advertisements putting over wartime messages under the heading "Old Bill says...". For this campaign the character was dressed in a special constable's uniform.
The original vehicles used by the Flying Squad all had the registration letters BYL, so the squad became known as 'the Bill'.
The London County Council at one time registered all police, fire and ambulance vehicles with the letters BYL
According to old Etonian illegal gaming club organizer and author the late Robin Cook ('Derek Raymond'), 'old bill' is a racing term for an outsider or unknown quantity. From the point of view of the underworld, police would be outsiders
Despite all these suggestions, the earliest documented usage traced by the Metropolitan Police Historical Museum is from 1970 and 'Partridge's Dictionary of Slang'. Without giving citations the book dates "Old Bill" from the 1950s "or perhaps earlier". So the term may possibly be post W.W.2.