To be an offensive weapon one of three conditions must be met:
1 - design
The item is DESIGNED to be a weapon. Eg. Fairburn Sykes commando knife or a sword
2 - modification
The item has been MODIFIED to be a weapon. Eg. Bar of soap in a sock or a baseball bat with 6" nails through it.
3 - intent
The person in possession of the item demonstrates or expresses the INTENT to use the item, regardless of what that item may be. Eg. Rolled magazine or ANY knife. Intent can be demonstrated by words (eg. Saying "I have this rope and I'm going to strangle you with it"), by actions (eg. Waving a butterknife around in a threatening manner) or any combination of the two.
This falls under the Prevention of Crime Act 1953.
More details in the link below (sorry hyperlinks don't work from my phone):
http://www.cps.gov.uk/legal/l_to_o/offensive_weapons_knives_bladed_and_pointed_articles/
Remember that all Acts are "clarified" (aka interpreted with a personal bias) by case law. This can change the detail of the Act by setting a precedent in law. For example, DPP vs Harris, 1995, set the precedent that lock knives are considered to be fixed blades for the purpose of Sect 139, CJA, 1988, exemption for sub 3" folders. Even a 1" keying folder needs a reasonable excuse to carry if it is a locker. And there is a lot of disagreement over multitools. I'm not aware of any caselaw, yet!
There was caselaw last year where an elderly man was convicted of having an offensive weapon after he made threatening remarks in a pub (IIRC). He did not have a weapon in his hands at the time. The weapon was a locker in the glove box of his car outside which was found when the Police searched vehicle.