You can buy a kitchen knife - just not if you are under age. Not it's perfectly legal for an adult to buy one for a budding cook - all the age ban does is put a 'responsible' adult in the loop.
You also can't carry one in public without reasonable cause - which in the end is decided by a judge.
Chefs can typically get away with carrying their knives (they get very possessive over the care of their own knives and so won't leave them in the kitchen) if they're in a knife roll and in a backpack or similar.
You also can't carry one in public without reasonable cause - which in the end is decided by a judge.