There's nothing in UK law that prevents you from doing this. Bring along a cook book and store the knife securely (and keep it in your bag) and you're going to be fine. If you get stopped by the police mention it straightaway and move from there.
The legislation is written broad enough that discretion is possible in cases like this. Where it's going to look funny is when you're stopped with it in a pub at 9pm on a Saturday night.
So yeah I see both sides (I might go for a beer down the local after cooking on the way home with the knife for example), but really there's not much wrong with your knife laws IMO.
This is also true, I certainly think if you're a white middle class person taking a knife to a friends you're going to get off easier than an someone from a ethnic minority in Tower Hamlets.
It also results in insane things like this [1]. I'm not sure if there's a better way though, it seems much like democracy it's the best of a bad bunch.
1. https://www.telegraph.co.uk/news/uknews/3165489/Gardener-arr...