Stop and search:
Police officers may stop you, and have the right to search any person or vehicle, if they suspect you of an offence - including carrying an offensive weapon. Weapons regarded as offensive include, but are not limited to, the following:
* flick knives
* gravity knives
* samurai swords...
it's a long list
but other types of swords aren't on it.
They can decide that just about anything is being used as an offensive weapon, even a screwdriver. Eg. Chefs knives can be counted as offensive, unless you can prove you have a reason to be carrying them.
Some things are now classed as offensive automatically ie samurai swords and you would never be able to convince anyone of a reason you should have one in public.
Official historical enactments, drama productions and sporting activities may be exemptions, but I would imagine that if you are wandering around town half cut on a Saturday night* it would be difficult to prove you were on your way to one,
Edit: *as Dan found out
If he had done that post 2008 he'd be straight down the nick...