If in doubt: Read the pertaining legislation, the bottom line is that if you are ever reported for an offence you are reported to be contravening a piece of legislation.
So, if you actually read the legislation rather than twaddling about what you think the legislation says or implies then you will find you have much more latitude in actually carrying knives in a public place*. In spirit the law requires that you have lawful purpose or reasonable excuse to be carrying what you are carrying - knives or baseball bats.
I shall give some examples, as a former plod, of what 'might' have happened in set circumstances:
1. If I had seen a chap dressed as Ray Mears wandering into Tesco with a bushie on his belt, I would have asked what he was doing locally. If he had told me he was camped around the corner communing with badgers I'd have asked him to take the knife off his belt and put it in his pocket whilst in Tesco.........he has a 'REASONABLE EXCUSE' [This is a legal term].
2. Chap wandering down the road in cammies carrying a machete. Here you would probably find yourself looking down the business end of an MP5 when you are asked what you are doing. Alternatively, a good plod would make sure he stood well back on the other side of a car before shouting over to ask what he was doing.
3. 03.00AM a call from a household that a burglar has been apprehended. On arrival there is a Paramedic crew dealing with the burglar who has a laceration to the skull and a broken arm. He tells you that the householder went for him with Mr. Baseball bat. When speaking with the householder you slide in a question about his prowess at the game of baseball, he tells you he does'nt play. You then ask why he has the baseball bat. He tells you it is to take care of intruders..........WRONG ANSWER. This immediately makes the baseball bat an offensive weapon and depending on the prosecutor and how far he wants to push it may result in the householder doing time.
4. A chap comes home. He pats his dobermann on the head. He notices his doberman is sort of half choking, bit like a furball. He gives the dog a hard slap to help out and the dog coughs up two [2] fingers, down to the first joint. 'Kin hell. He looks around and finds an open window but no intruder. Shortly after there is a knock at the door the nice policeman wants to report him for having a dangerous dog.........believe it or not, the burglar made a complaint.
The law is an bottom, but the law also works both ways. Remembering I used to be a plod, most plods are as dim as the day is long - you do not even need to be able to read and write to be a plod nowadays, honest - ask me and I'll explain. How many coppers do you think have actually sat down and read a piece of legislation from beginning to end? Record numbers of graddies but are they joining plod, short answer 'no'.
My advice to you, read the law, know what your reasonable excuse is and fight your corner if confronted - 9 times out of 10 if you quote legislation plod will back down.
http://www.opsi.gov.uk/acts/acts1996/1996026.htm
http://www.opsi.gov.uk/ACTS/acts1988/Ukpga_19880033_en_12.htm
http://www.opsi.gov.uk/ACTS/acts1997/1997021.htm
DISCLAIMER: These are my ramblings. They are not intended or implied as advice or guidance, you should always seek clarification from a suitably qualified authority or person - Personally I would write to the Chief Constable explaining what I do where I do it and what I intend to carry, trust me he'll write back.
* Public place: A place to which the public have access by payment or otherwise - for example: a footbal match; Tesco; public car park; or, the Bush moot.