Being a participant in historical European Martial Arts I have heard much discussion about the legislation. Admittedly none was in favour.
It has been mentioned that there was a slight variation on the law that specified whether the blade was sharp or blunt.
If it was blunt as used by most re-enactors or recreators then it was exempt. However, if it had an edge then it was classified as offensive.
I have yet to meet anybody who studies historical fencing that would be likely to go on a rampage with a blade. I agree that the law is silly. However, it is also ridiculous that any idiot can by a sharpened blade from a sports store like 'Planet Max'.
It is worth noting that as a serious weapon most of the blades from the sports suppliers wouldn't last more than a couple of blows in a bout with another weapon whether of the same quality or 'combat ready'.
By the way you can't swash-buckle with just a sword. You need a buckler (small rounded shield) on hand as well. The phrase originates from the 16th century where gangs of youths (much like todays trouble makers :-) ) would roam the streets 'swashing' swords against bucklers to announce their presence and challenge for a fight.

Sure a sharpened edge is low tech, however, there are some even more basic options that don't require much tech.
Someone who was serious about killing someone would in fact consider options other than a sword.
A sword is too cumbersome for most people, rather hard to conceal on ones body, a bit expensive to be used disposably, and is not quite the 'ultimate' weapon it is perceived to be.
According to a copper I've spoken to the commonest impaling device is actually a screwdriver. It doesn't require much in the way of sharpening. Just having a wedge and a stiff shaft is all that's needed to penetrate. A fine edge is more essential for cutting blades like for example a kitchen knife.
In terms of effective melee weapons one can come out quite well with stiff shaft like perhaps a walking stick or a pvc pipe.
So yes I agree the intent of the legislation is an over reaction to the perceived threat of swords being on the streets.
Following the concern of the legislation they might have to ban walking sticks from all those geriatric gangsters and watch out for those gangs of home-improvement hooligans...:-)