I know there are more and more guns being carried by British Police all the time, but for a long time they were unarmed. How long as this been true for? Why aren't they armed?
As I was thinking about this question the entire notion of the British police system started making less and less sense, Why is London's police called Scotland Yard? Bob doesn't sound very Scottish, but still they're all called Bobbies? Are there other police forces around the country or is it unitary like their parliament? And if they're so good why does Sherlock Holmes seem to solve all the really tough crimes in London? ^^^^^^not ^^^^^^an ^^^^^^entirely ^^^^^^serious ^^^^^^question, ^^^^^^but ^^^^^^the ^^^^^^origin ^^^^^^of ^^^^^^my ^^^^^^interest ^^^^^^in ^^^^^^the ^^^^^^subject
and where does the Sherriff of Nottinham come into play? Seriously if he's around with King John, there aren't any parliaments around to make laws, and really he doesn't seem like a law man, more like a tax man to me.
Really it's all very confusing.
Basically, I'm interested in the history of Police in Britain, I love reading what the fantastic contributors here have to say, but I also like reading, so there's that if you have sources that are fun and interesting
Someone else will undoubtedly be able to answer this better than I can, but I can help you out with a few points. The answer to your main question is yes: British police have always been unarmed, or perhaps more accurately, they have never been routinely armed.
The modern police force goes back to 1829, when Sir Robert Peel, then Home Secretary and later Prime Minister, founded the Metropolitan Police. They are still the main police force in London, and their headquarters are at Scotland Yard, named after a street, as /u/Second_Mate mentions. Sir Robert Peel's name is the origin for the nickname "Bobbies" (and less common nowadays, "Peelers"). The reason they were never armed is that they were founded on principles of policing by consent, as a civilian alternative to law enforcement by military means: you can read the Nine Principles of Policing, on which the Met was founded, on Wikipedia. More police forces were established around the country following on from the Met, which answers another of your questions, and right up until today these principles have all remained important ideals about what the police should be.
The Robin Hood legends are set centuries before the concept of a professional police force even existed. In medieval times the sheriff was the royal representative in each county: this was a powerful position with a range of duties, including legal and financial functions.
The modern Police services in the UK are modeled on the Metropolitan police in London. The Met was founded in 1829 and was deliberately founded as a civilian organization. Before this there was very little in the way of organized policing. If someone had committed a crime there would be a warrant out for them and they would have to be taken to a magistrate who would sentence them. Victims or families of victims would hire 'thief takers' to drag miscreants in front of a judge or magistrate and particularly heinous criminals would have 'the constable' assigned to them but a large amount of crime went unpunished. In times of serious unrest the military would be sent out to restore order. This is where your Sheriff of Nottingham would come in.
In the 1820s mostly as a result of increasing urbanization and clamor for political reform there was a period of considerable unrest and the military was used to put down several protests very bloodily (peterloo massacre etc.). And due to the distrust people had of the Army (and because politicians saw the cities as powderkegs of dissent) There was a deliberate choice to make the police force as different from the Army as possible.
This meant they made the uniform a nice rich dark blue rather than the bight red of the Army, they didn't carry swords or guns. Just a big heavy stick and a whistle. They didn't have military ranks ( I think sergeant was added later) The whole idea and philosophy was that these officers would be members and participants in the community rather than antagonists to it. The founder was a guy called Robert Peel which is why his new 'policemen' were referred to as 'Bobbies' or 'Peelers' The phrase that Peel used to describe his philosophy was 'policing by consent' that you need the officers to be part of the community that it polices.
Although that attitude has waxed and waned over the years it's still a core idea of policing in the UK and has driven many high profile policy decisions (such as cannabis decriminalization in Brixton)