Precisely. I could entirely legally carry my knife roll on the train up to my friend in Leeds, and if stopped explain "I'm intending to cook whilst there, these are my knives for doing so". The police have every right to corroborate this story, but there is no crime there.

The thing I've potentially fallen foul of is a chunky pocket knife I keep with my climbing/camping gear bag and have on occasion forgotten to remove before going to indoor walls in London. I suspect I'd potentially be told off a bit for that, but again no fear of being charged with anything.