Here in the UK, the carrying of ANY offensive weapon (not just a knife)is prohibited unless one has a good reason.

A good reason NEVER includes self defence. Good reasons can include being a chef or cook, or needing a knife for ones work, or moving a knife from one place to another such as taking a newly purchased knife home, or moving the contents of a home to a new address.

The police have very considerable discretion as to what is permitted.

In the past, the carrying of a small folding pocket knife with a non locking blade of less than a certain size was permitted, but this is no longer the case.
A Swiss Army knife USED to be permitted, but is now regarded as an offensive weapon unless one has a good reason to carry it.

In practice, the size of the blade and whether or not it locks can be a deciding factor.
For example a Leatherman tool with a locking blade is looked upon less favourably than a non locking Swiss army knife. But this DOES NOT MEAN that the non locking blade is automatically "legal" or "permitted"
The circumstances of carrying the knife also make a great deal of difference. A chef carrying a number of knives too and from work in a bag or box should be fine. The same chef carrying a single kitchen knife to the local bar might well be found guilty of carrying on offensive weapon.
A scout carrying a knife well packed inside a backpack or other luggage on the way to/from an outdoor activity should be fine, the same scout carrying the same knife on their belt MIGHT attract unwelcome attention.
An engineer carrying a Leatherman tool in a tool box should be fine, carrying the same Leatherman tool loose in the pocket MIGHT attract unwelcome attention.

No one under 18 may purchase a knife, a 17 year old living on their own should ask someone 18 or over to purchase them a kitchen knife or DIY tool.
Retailers are required to ask for proof of age before selling a knife, unless the purchaser is clearly over 18. IME retailers DO check before selling pocket knives, but often don't bother for kitchen cutlery or workshop tools, though they should check before selling any knife or "bladed tool".
Almost any type of knife or bladed tool may be lawfully sold to anyone 18 years or over, though a few types that are considered to be especially dangerous and/or to have no legitimate use are banned outright and may not be sold, manufactured or imported, IIRC there is an exemption that permits museums to acquire such items.