Some people struggle to understand UK knife law and some don't. It's really a lot more simple than the official documentation makes it seem.
This knife here (my edc) is 100% legal to carry at all times apart from in places that are subject to different rules, so pubs, clubs etc.
As shown in the video, you must be able to fold the blade away just by pushing on it. So no locking mechanism or fixed blade. The only other rule on what you CAN carry is that the cutting edge must be no longer the 3 inches.
As for what you can't carry in public, without a reasonable need, i.e to do your job, it's basically everything outside the above mentioned parameters. No locking blades, no fixed blades and no folding blades with a cutting edge over 3 inches. If you think you have a legitimate reason to carry something else then it's entirely your responsibility to prove as such. If you can't prove it, you can't carry it.