North Yorkshire Police announced the warning message after receiving three reports of the scam in a 24 hour period on January 12.
Officers said the scammer will call the victim claiming to be from the police, and in the most recent cases, as the bogus 'Sergeant White from the Serious Crime Unit at York'.
Andy Fox, North Yorkshire Police's Financial Abuse Safeguarding Officer, said: "This is a fraud which will simply not go away and unfortunately one which continues to be highly effective.
Scarborough officially smashes temperature record as Met Office confirms new hottest day
Post-war asbestos bungalows to be demolished in Scarborough as plans for new terraced homes approved
Firefighters respond to arson attacks in Scarborough and fires near Malton and Whitby
RNLI issue weever fish warning for Yorkshire coast
Yorkshire Water announces first hosepipe ban for more than 27 years – with fines of up to £1,000
"The fraudsters add a layer of credibility by having another scammer pose as a second police officer which is all part of their manipulation to convince the victim they are real."
In this instance, the scammers add another layer to the deceit by transferring the victim to the bogus 'Officer Timothy Mason' from Brixton Police, who claims to be with an arrested individual.
The caller advises the would-be victim that they need to immediately attend the bank and withdraw all money from their account in cash. A ‘police officer’ or courier will then come to their home to collect the cash and take it for safekeeping.
Officer Fox added: "You might read this and think you’d never fall victim to something so obviously a scam but you would be surprised by just how many people lose tens or hundreds of thousands of pounds to these calculated individuals.
"They work hard to be as convincing as possible and no one is immune from their approach. These fraudsters also use a technique called number spoofing, where anyone can make their phone number look like a legitimate one.
"Remember, the police or your bank will never contact you and ask you to move or transfer money. If you receive a call of this nature, hang up immediately. If you want to double check whether it is a legitimate call, use a different phone to ring your bank’s customer service phone number."