Background Check at British Heart Foundation

I can totally understand them wanting to do criminal record checks on people but I think they have a cheek demanding references. This is not paid work after all.

They always to a background check to see if they can trust you in the store on your own or if they cannot trust you in the store on your own. (I'm trusted alone)

yes but not likely as a paid staff as they are always looking for volunteers and will aid you in looking for new work, or getting a paid job within the business and I know of two ex volunteers that achieve paid positions while most leave to find paid work after a few months - years