Drago is not the only ex Polis on this forum! (But my experience is now 20+ years out of date. Despite that, the law has not changed).
Here is the legislation relating to the carrying of offensive weapons in the UK....
Prevention of Crime Act 1953
The relevant wording is "Any person who without lawful authority or reasonable excuse, the proof whereof shall lie on them, has with them in any public place any offensive weapon shall be guilty of an offence."
A bike lock (chain or whatever) is NOT an offensive weapon on its own. There are items which are MADE to be offfensive weapons (e.g. knuckleduster); INTENDED to be an offensive weapon (e.g. a knife if being carried without lawful authority or reasonable excuse); or ADAPTED (e.g. a bike chain wrapped around your hand). So unless you or your friend intend to walk down your local High Street swinging the lock/chain around in an aggressive manner looking to clobber someone with it, you are NOT committing any crime. Pretty much any item can be adapted to be an offensive weapon. The keys in your pocket, your bike pump, drinks bottle, helmet, whatever; the list is endless. So no need to worry.