The caller then asks the victim, who is often elderly, to pay a fee in order to release the refund and tells them to make the payment via international transfer service Western Union.
One woman in the Shrewsbury area lost £125 after making a payment, having never received any refund.
Police Constable Claire Challinor, who is investigating the incidents, warned people that the calls were not genuine.
“Banks do not contact their customers and offer them a refund on any charges,†she said.
“If you believe you may be entitled to a refund, it is down to you to contact your bank directly and request one. The banks do not charge a fee for refunding any charges.
“Anyone who claims you are due any kind of refund and asks for personal or bank details or for you to send or transfer any money should be treated as a scammer. Never give them your details or send any money.â€
Western Union is a legitimate international money transfer service, which the offenders are using to get the victim’s funds deposited into their own accounts abroad.
“The bottom line is, anything which sounds too good to be true probably is,†added PC Challinor.
“People need to be alert and suspicious of anyone who claims they are due money back but that a fee or bank details are needed. Do not give either and hang up immediately.â€