Many people are not reasonable which is why I dislike such subjective laws. You forget to take the knife out of the car or the bag and you're screwed because you don't have a "valid reason" for possessing one, terrible lawmaking quite frankly.
However the way the law is worded means that the Police can use their discretion.
If you can reasonably say "I was at a BBQ the other day and forgot it was still there" you're pretty covered, assuming you're not known to the police for violent offences involving weapons.
That is the only way this sort of law can work, otherwise it's either legal to carry a knife all the time, or it's illegal to carry one at all, or criminals will learn very very quickly how to carry one and be able to claim they were legal.
The real problem imo comes from where the law tries to be too exact - for example under your example if you had to have a specific reason for (that particular) knife at that exact time you would be really screwed, whilst someone who is fairly obviously up to no good but thinks to put the knife with some bbq tongs and a 99p disposable bbq would be fine.
I would much rather "wooly" wording on laws that allow the police, cps and ultimately the magistrates or jury the ability to decide if the law as it was meant was broken, than a pure black and white law that may be much more complicated in the real world to follow, and means that there is no discretion or common sense involved.
Remember, if it were to go to court, the CPS would have to convince 12 normal people that you broke the law intentionally beyond reasonable doubt, that is quite hard to do when you cannot prove intent or a reason to break the law and the defendant has an understandable reason for what they have done (I doubt there is anyone who drives who hasn't forgotten to take something out of the boot at one time or another, especially after a day out or a holiday).