Gun ownership only really became a factor in Britain during the 16th century. Prior to that, a sort of "right to bear arms" did exist but this was rooted in the monarchy's desire to save money when raising armies. The idea was that every fighting man should possess weapons and armour befitting their social class that they can take to war (spears for peasants, suits of armour for knights, etc). Men who turned up without weapons had to be equipped at the monarchs own expense, which was not something they were eager to do. Armed peasants obviously created a threat of uprising against monarchs but this situation could be manipulated by local lords to their own benefit. Despite this, rebellions were common in British history and a constant concern.

The first real scare for the monarchy in relation to gun ownership was two high profile assassination of Protestant political figures by firearm during the reign of Elizabeth I. In a space of 13 years, the Regent of Scotland and the Prince of Orange were both assassinated by lone gun-men using a rifle and pistol respectively. Elizabeth I, as a major Protestant monarch, was wary of assassination by another Catholic gun-man so instituted the first ban of fire-arms (only near Royal palaces) and further laws in the 17th century focused on disarming Catholics while protecting gun ownership for Protestants.

Since fire-arms weren't widely manufactured or cheap to buy, common people didn't have much access to them. However, army regiments of the 17th century were often raised privately by wealthy land-owners, merchants and aristocrats for the monarchy (or against the monarchy in the civil wars). They would pay to import thousands of firearms left over from European wars to arm British regiments. Since they were technically all owned by this single individual and could be sold on, they weren't perceived as personally owned by each soldier and would attempt to disarm their own regiments. However, this didn't stop many soldiers from simply taking them home. Two additional factors made gun ownership even more common:

1. Mercenaries: Like every other European country of 17th century, Britain relied on mercenaries to bulk up their armies. Scotland in particular sent thousands of mercenaries to mainland Europe to fight in the religious wars there. As professional soldiers, they came home with their weapons and, more importantly, their experience, becoming a major factor in the British civil wars.
2. Standing armies: Cromwell's New Model Army was the first British standing army in the 1640s. These men became dedicated to a military life and were an active force across the entire British Isles for 15 years. Professional, permanently equipped soldiers like this became the core of the British military and the re-instated monarchy realised that their army was capable of dethroning them, ultimately handing over all control of it to parliament.

The Jacobite rebellions from in Scotland during the 17th and 18th century definitely benefited from a reserve of fire-arms personally owned by Scottish mercenaries and ex-soldiers, but this was marginal and completely inadequate to opposing the British army. Most of their weapons in later uprisings were provided by France or purchase personally by the Stuart pretenders. Each Jacobite uprising was followed by an effort to disarm the Scottish Highlands with the final Act of Proscription in 1746 being the most effective and brutal.

You can draw a direct link between soldiers returning from major wars and new firearm legislation. The Napoleonic Wars, WW1 and WW2 were each followed by Acts that sought to recover lost firearms and punish those using/found with them (I believe the American Civil War created a similar problem). However, these restrictions never fully outlawed gun-ownership and were usually trying to crack down on something else. 19th century politicians were more concerned about illegal poaching or using gun control as a means to generate revenue for the government through licences. Early 20th century gun control was trying to tackle more serious issues like organised crime or the smuggling of firearms into Ireland for use in the civil war or terrorism (a problem than continued into the 90s). However, some fairly disgusting acts of domestic terrorism using legal weapons (see Hungerford and Dunblane) in the late 20th century fully turned the country against the idea of wide-spread gun ownership. Amnesty programs recovered over 100,000 firearms in the 90s and the government spent millions compensating owners. There are still millions of legal firearms in the UK but they are strictly controlled.

However, George Orwell's quote is not referring to privately owned guns. It is often mis-quoted to push a gun-ownership position to people who respect his politics and work. Orwell is actually referring to rifles in the homes of men enlisted in the Home Guard, which was a citizens militia established by the British Army as a last line of defence in case of an invasion of Britain by the Axis powers. It was made up of men who were too old, young or otherwise ineligible to join the Army, it even enlisted women mid-way through WW2. They were trained by the Army to defend key locations in the event of invasion and were armed with whatever the British Army did not want/need, leaving them badly equipped for much of WW2. Orwell was commenting on the nature of citizen militia's in totalitarian states like Nazi Germany and Soviet Russia, claiming that they could not establish something like the Home Guard as it could only exist in a free democracy. He is suggesting that a totalitarian government would not trust the working man to own a gun in case they rose up against them. Unfortunately that is a very utopian idea which doesn't fit with the fact that the Nazi party actually loosened gun laws and instituted many programs similar to the Home Guard that handed out weapons to civilians (see Volksstrum). The quote was from a newspaper article in 1941, so Orwell's intention was probably to defend the Home Guard and encourage working people to join, he probably wasn't fully-aware of the similar institutions in Nazi Germany. Orwell's advocacy of gun-ownership also fits more with the Swiss model of mandatory military service rather than a defence of private, individual ownership which is the common debate in the US.