It's more that British law with possession of weapons is very focused around intent.
Carrying a knife for 'self-defence' is still regarded as carrying a weapon with intent to use it to threaten, injure or kill another person. And that is the actual thing that is illegal.
Preemptive self-defence is not allowed as an excuse. Heat of the moment self-defence is fine, so if assaulted in your kitchen pulling a knife off the kitchen table would be perfectly allowed, though will probably result in you being temporarily detained by the police for a bit of time whilst they do the initial investigation and questioning (to both prevent you from fleeing or interfering with any evidence, allow them to question you, and to protect you by making sure no reprisals are likely). British self-defence law is actually surprisingly permissive on that front, despite what the newspapers like to claim. Benefit of the doubt is actively encouraged for judges in areas where it may be considered legally grey.
Hence, if a police officer sees someone with a knife out of packaging, or searches someone and finds one, and they don't have an immediate and obvious practical reason to be possessing it, they have to power to arrest/detain them and/or seize the knife under the reasoning that it's possession of a deadly weapon with intent.
For example, Scout Leaders are allowed to take a variety of knives with them on the scout camping trips, but are expected to go be responsible with them at all times (obviously) and to go straight home and put them away in a secure location as soon as they are done acting as Scout Leaders.