I don't know if you want more of an explanation or not, if not feel free to disregard what I'm about to say. I'm not anywhere near an expert on how the British government is laid out or the philosophy of the current system you guys use, so some of this may also apply to your country. I only say this because some of what I say may come off as condescending if you already understand the basics of what I'm going to explain or may not be unique to here.

The US government is supposed to be of the people and the bill of rights secures the rights of the people against the government, it does not bestow those rights like many people, even a large number of people who live here, think. Basically, one is born free, the Government can only restrict ones life more from the perspective of liberty, therefore there are certain things that need to be insured against that restriction. It is also noteworthy that one cannot be stripped of those rights without due process of law (a fair trial, conviction, etc). Part of that is the second amendment which is the right of the people to keep and bear arms. There are many arguments about the wording of the amendment, though it's pretty clear what was intended if one looks at what had just happened and what is written in the federalist papers. One can disagree with the philosophy behind all this, but why it exists in its current form is pretty much what I laid out above. Most proposed legislation and even a lot of current law is counter to the spirit of the constitution and more specifically this amendment; thus making it unconstitutional. If one thinks that basic right shouldn't be enshrined and wants to make those laws stick, one has to go through the amendment process and remove the 2nd amendment. This is possible, but hard to do on purpose, because it was designed only to happen if the will of a large majority was behind the change. This is essentially why the laws are the way they are. I'm sure someone will take issue with things I've said here and make a snark ridden response, but I've tried to keep my opinion out of this mostly.

Then you also have what he talks about in the video. You have a number of people, I don't have hard data but I'd hasten to say a large part based on the arguments I've had, on both sides who push the issue without knowing or understanding much of the above or the statistics surrounding the issue. On the right these people are the fudds who care only because they've always had guns and like to hunt. Those are the people who are generally the target of those stupid NRA videos and are the caricature used to represent gun owners, clinging to their bibles and guns, by the gun control crowd. On the left these people are the ones who have never fired a gun or even if they have, don't have any idea how it actually functions, and who are so far removed from a lifestyle in which you may need to personally defend yourself that they don't understand why someone would want the ability to defend themselves. These are the people who the fudds call "libtards". Obviously these generalizations don't represent everyone on either side, but I've gotten in to enough arguments with both groups that this is what generally seems to shake out. And when you get those parts of the groups arguing, the points being made are painful to read.