Incorrect. They are, most definitely, illegal to carry without 'reasonable excuse'. Eg, the locking blade on a multi-tool, if your job demands its use, or if you're in the middle of the woods doing camping related stuff. But if you mean for every day carry, they're illegal to carry in this context and you'll find yourself arrested and most likely charged with posession of an offensive weapon. Lock knives are as legal as fixed blade knives, its totally context dependant, basically.
As for the first knife, the one this thread is about, "butterfly knives - where the blade is hidden inside a handle that splits in two around it, like wings; the handles swing around the blade to open or close it" - the law makes no distinction as to how exactly the handles encapsulate the blade, and it doesnt matter - when held, it is locked and therefore counts as a lock knife. But also, legally, it's a butterfly knife/ballisong.
The cold steel one is illegal in the uk for the same reason, the handles split in 2 and fold around it like wings. One handed opening isn't part of uk legislation on that point. The blurb relates to US law, which I assume must be different.
It sucks, and I wish I could carry a decent knife, but basically if you want to be legal then its basically a pen knife or ukpk
