You can have a bladed article on your person at a place of work, if required for the purpose of work, or at your place of abode. An abode can be your home, a vessel of which you reside, or even a car or caravan that is occupied and parked (completely stationary) for the purpose of habitation with some permanency.
You may transport a bladed article to or from a place of work, for the essential purpose of work, as long as reasonable precautions are taken and the journey is directly to and from work. For example, a chef taking knives to work, secured in the boot of a personal vehicle, without stopping at any public place during that journey without exceptionally good reason.
A big mistake people make is often this; carpet fitters, with a Stanley knife equipped to their tool belt, popping into Greggs for lunch!
Also, there is a difference between "possession and "has with them".
"Has with them" does not mean you have it with you at hand. In case law, someone got into trouble for having a knife in their car on, I think, a camping trip. They were within 50 meters of the vehicle, and knife, and was deemed it was both in their possession and had it with them, as being within 50 meters or less means you have reasonably easy access to that knife.
Technically, we are all in possession of a knife. Say you drive to work and leave your fancy kitchen knives in the wooden block... you possess a knife! You just don't have it on you!
So the offence is typically complete when someone "has with them" (within 50 meters), and are "in possession" (it is theirs, it belongs to them, they know it belongs to them), of a pointed/bladed article, and in a public place of which the public have access to at a material time paid or otherwise, and without reasonable excuse or lawful authority, are guilty of an offence.