There's no single answer to this, but the date usually given is 1829, with the establishment of the Metropolitan Police by Sir Robert Peel, the then Home Secretary. It's worth mentioning the Peelian principles which set the character of the force as keepers of the peace rather than law enforcement officers.

There were precursors such as the Bow Street Runners (est. 1742, reporting to Bow Street magistrates) who did not patrol and were solely used to arrest suspects. Prior to that there were paid and unpaid constables.

hi! there's room for more on this, but meanwhile, you can get started on these previous posts

• At what point did societies begin making a distinction between military and police?

• When did police forces start to become their own unique professions, and not simply militias/armies/levies?

• What was law enforcement like in cities of the middle ages? Was there any distinction between law enforcement and soldiery?

• Why was the Metropolitan Police Force established by Peel in 1929?

• Have British Police always been unarmed?

In 1829 British conservative politician (and later prime minister twice from 10 December 1834 to 8 April 1835 & 30 August 1841 to 29 June 1846.) introduced the Metropolitan Police Act 1829 (excluding the City of London and only serving London at this point) this act established the first major police within the UK.

However, "The Met" may have been the first major police force in Britain, but it wasn't the first police force in the UK, It's predecessor River Thames Marine Police Force (It was formed by Magistrate, Patrick Colquhoun & Mariner, John Harriott in 1798 to tackle theft in & around the Thames, it ran until 1829 when it merged with "The Met"). The river police did eventually turn into the Metropolitan Police Marine Policing Unit..

There have been several revisions to the original Metropolitan Police Act of 1829, the majority of these changes took place between 1829 & 1895 and are conveniently known as the * Metropolitan Police Acts 1829 to 1895*.

Originally the Metropolitan police were known as "The Peelers" or "Bobbies" after Sir Robert Peel. The idea came from the need to improve public law & justice in Victorian England. By September 1829, 17 divisions had been set up with 144 constables & 4 inspectors each, not much when you think of the size of London in 1829-1830.

At first the quality of the officers were poor, out of 2,800 possible new policemen, only 600 eventually kept their jobs with one police officer losing his job after just 4 hours in the role. This prompted Peel to summarise his ideas on what an "ethical police force" should these are outlined in the Peelian Principles.

By 1856 *County and Borough Police Act 1856" was introduced to make it compulsory for a police force to be established in every borough & county in the UK.

If you have any more questions don't hesitate to ask.

References:

The Official History of the Metropolitan Police. Robert Peel: A Biography. Victorian Crime & Punishment: The Development of a Police Force. Criminal River: The History of the Thames River Police.