[user5994461]

You never list references from your last job.

You don't want your future company to call your current company to give them a heads up that you are leaving.

For this very same reason, companies never ask for reference from your current job.

[mdpye]

In the UK, you tend to get an offer conditional on references, and you only provide them once you've given notice to your current place.

[user5994461]

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.

[macspoofing]

>For this very same reason, companies never ask for reference from your current job.

Sure they do. They just give you an offer first and make it conditional on a reference check.