"So why all the hype? "
This is what the anti-gun lobby does -- comes up with problems where there really aren't any as an excuse to reduce gun rights. If you listen to these people, you'll get the impression you're in imminent danger of being shot into a fine mist by machine-gun-wielding misfits on each and every block. Ultimate goal would be to restrict *some* guns, then use that a starting point to restrict *more* guns, and so on.
The three major problems as I see it (disclaimer, I have no guns, I just am a libertarian so I don't believe in unnecessary restrictions):
1) As you're seeing now in Britain, if guns are made illegal then only criminals have guns. I read an article saying a "Saturday Night Special" in Britain is only about double the cost as in the US (something like 150 UKP) so if a crim wants a gun they can have it, and since all these guns are black market there's no realistic chance of tracking a gun down if it was used in a shooting. Despite what the article asserts, guns here usually are registered. With that said, quite a few shootings here are gangbangers shooting each other up, and a lot of those guns are illegal (not illegal mods like machine guns, but people carrying a weapon without gun permit, unregistered guns, etc.) so then you are at the same point of not being able to find the weapon.
2) Often times, these objections are not fact-based. A big problem in the US, with our relatively broken two-party system (two nearly-identical centrist parties but each party is sure they are TOTALLY polar opposite of the other), there tends to be these shows and channels and web sites that are like an echo chamber echoing more and more distorted information to meet their political agenda. A lot of people (both pro and anti-gun) are not just uninformed, they have very inaccurate information because of this.
3) Constitutionality. Gun rights are a constitutional guarantee, and anyone saying they just want to restrict them *some* indicates they are willing to ignore the constitution and the bill of rights. These are often the same people who want to start "balancing" people's rights (meaning removing rights) in other ways. There is a defined mechanism for passing a constitutional ammendment, if these people truly want to restrict a few defined types of guns and that's it, enumerate them and get an ammendment passed to do it.