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.
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.