While you'd definitely get some weird looks, I don't think people would generally get in trouble if carrying around a sword. I could be wrong, having never carried around a realistic looking sword in public, but my dad used to bring his WWII katana to classes for show and tell when I was a kid (admittedly, that probably wouldn't be allowed nowadays, but that's just in schools...and you know what, maybe we Americans are getting as paranoid as you Brits. :).