Typical, I just typed a long response to you MMN and the computer just had a fit and deleted it. My understanding of the safeguarding responsibilities, as outlined in many documents but you could check out Safeguarding vulnerable groups act of 2006, the children act 1989, and the safeguarding act 2014, I haven't read it all, most of my understanding comes from teacher training. Vulnerable groups relates to children, young people and vulnerable adults.
As for the exact legislation you ask for, no I can't. But:
In England the law states if you work with young people you have a duty to keep them safe.
My understanding of the things I have read over the years are that:
if you are staff or volunteers (or a supervisor overseeing the previous two groups) running "activities" for "vulnerable groups", for 4 or more days out of a 30 day period or overnight then keeping them safe means a safeguarding system needs to be in place in order to fufill the requirement above.
But it could be my interpretation that's hinky.
I wouldn't want to be the lawyer trying to defend a private business from an allegation when it's discovered they were supervising young people and their staff hadn't been checked out properly.
Shops don't run activities or supervise children. Almost all of the airsoft companies I've seen simply don't allow unaccompanied young people and therefore aren't needing to supervise the young people themselves.
If it helps, to get a taxi licence you need a DBS (the new version of a CRB).