By Bob Howard
BBC Radio 4's Money Box
There are guidelines for how banks should identify themselves
People called, apparently by their bank, and asked for their passwords or pin numbers, should not disclose them.
This police warning comes as dozens of people living in the Scottish Highlands have been targeted by fraudsters.
Most banks require customers they call to give them some information to ensure they have contacted the right person.
The banking industry says if anyone is unsure about a call, they should phone the bank back on a recognised number from a statement or bank card.
About twenty customers in the Highlands lost money after fraudulent calls were made over a six month period.
They were tricked into giving telephone banking details which allowed the fraudsters to transfer money into other accounts and withdraw it.
Detective Constable Stephen McCabe from the Northern Constabulary told BBC Radio 4's Money Box some have lost considerable sums:
"This is a scam that goes around on a fairly continuous basis.
"Some of the losses are in excess of between £10,000 and £20,000."
There are guidelines for how banks should indentify themselves if they make an unsolicited call, drawn up by the British Bankers Association (BBA) and the Information Commissioner's Office.
They recommend banks either offer a pre-agreed password to customers or suggest they phone the bank back on a clearly verified number.
Brian Capon from the BBA admits it is a difficult area:
"We've got the bank that wants to make sure it's really the customer it's speaking to.
"And the customer who wants to make sure it's the bank they're talking to.
"I don't think there's a simple, straightforward answer to it."
'Play it safe'
Mike Naylor, formerly of Which? and a commentator on personal finance, believes changes are needed:
"If banks want to make outgoing phone calls then they need to have a series of passwords or something else in place.
"They can't on the one hand say don't give out your details and on the other hand expect people to give out their details."
The main High Street banks all say they would never ask people to give sensitive information like passwords or pin numbers if they make an unsolicited call.
Det Con Stephen McCabe says if customers are unsure, it is always better to play it safe:
"If you are in any doubt at all, you shouldn't be giving out any information whatsoever.
"If you do get these calls, call your bank on their recognised number."
BBC Radio 4's Money Box was broadcast on Saturday,
10 January 2009 at 1204 GMT.