reference checks are useless. if you list HR they can only confirm employment. If you list your friends they going to say good things. if you list anyone else you are doing it wrong
That's absolutely not what's meant by "listing references". The OP is talking about listing reference, possibly on his resume or on-request, to companies he's prospecting.
The UK has a custom to perform an employment and criminal check by a 3rd party company when you join a new company (after you signed a contract and already gave your notice). That's unrelated.