A few years ago I got stopped in Liverpool Street Station after patting their drugs dog - he said they didn't know if the dog had indicated me or not. Fair play I guess, wasn't that concerned.
I also happened to have in my bag two knives, similar to this:
and
As soon as I saw him pull them out of my bag I cringed and thought, crap, never thought of that. Thing is, he didn't say word about it, and just looked through the rest of my bag briefly (was hardly a full search), gave me a bit of paper, and sent me on my way.
Now, this was about 22:30 on a weekday night at Liverpool Street Station - a very busy station in Central London.
Of course, what I didn't include in that story above was the fact that the bag he'd taken the knives out of also had a lot of very wet scuba gear in them - they were dive knives. I already had my defence in my head when I saw them - both knives were attached to my BCD. I dunno, maybe the PC was a diver.
This led me to query the status of knives with the email service at the Met (I can probably dig out the reply). The reply I got back was essentially as listed previously - you have to show just cause for carrying. To/from a dive training session for example would likely to be deemed OK (likely!), whereas carrying the same knives without any of the other gear in isolation and say while out to dinner would be deemed inappropriate and likely for action.
It's not an absolute offence - I.e. you did or you didn't. The terminology is something along the lines of that 'a reasonable person would make the choice that offence has been committed'. Subjective laws must be a minefield to police.