Police have issued a warning after scammers targeted five elderly residents.
Those contacted by fraudsters in Sutton were aged between 69 and 91.
They received phone calls from people claiming to work for a bank, who asked them for PIN details and wanted to collect their cards.
A woman aged 91 lost £2,000, while an 88-year-old man lost £250.
In the remaining cases the bank cards were cancelled before any withdrawals could be made.
The other three were based at Godalming Avenue, Wallington, Gordon Road in Carshalton, and Bristow Road, Croydon.
All of the victims were contacted between April 23 and 30.
In one instance a neighbour intervened and cancelled the cards after seeing a cab arrive at the victim's front door.
Police are warning residents that the scammers may pretend to be from the Serious Fraud Office.
They have also said the fraudsters might pose as police.
The purpose of the scam is to trick people into telling them their PIN number, before sending a cab round to collect their card.
Sutton Police are urging people not to reveal their bank details to strangers, and to hang up on anyone asking for their PIN.
They are also appealing to local taxi firms to report any suspicious calls, especially requests to collect brown envelopes.
The force are urging anyone who receives such a call to phone 999.
Victims of the scam should call police on 101.