Always be careful when talking to the police in situations like this - they are trained to get you to incriminate yourself.
The
laws for Stop and Search are that they need to suspect 1. a person matching your description of 2. carrying a particular object.
a
reasonable belief to suspect that you may be carrying something illegal or something that can be used to to commit an offence and you are likely to do so.
So challenge them, & if they can't give you this information, refuse consent to the search.
So for example:
> "We suspect a tall man with a beard in the area of stabbing someone; you are a tall man with a beard with a bag where a knife could be concealed'
lawful search
> "we were just hanging about & we haven''t got a collar yet today and you Look Like The Type so we're going to search through all your stuff, and if we find something illegal we'll nab you for it - we'll also check your wallet to find your name - oooh i see you have a knife here, and something to smoke, and..."
unlawful search
You should always refuse a caution - a caution sounds like you got away easy, but it goes on your permanent record and they have to do zero work, they're counting on you being afraid of court that they don't have to do the work of proving you guilty.
If the police say - 'we suspect you of carrying a bladed weapon because you look like a bushcraft guy, and bushcraft guys tend to carry knives' - that's borderline IMO, so make them take you to court and prove that they have 'a reasonable individual suspicion' based on your appearance that you have or are about to commit a crime. Make them convince a judge that a bloke wearing trousers with more than the usual number of pockets is legal grounds for suspicion. If they know their case is on shakey grounds, they'll drop it.
A lot of the time, they are relying on you incriminating yourself or being intimidated. Know your rights, and make them do their job properly & within the law.