Fraudsters have targeted elderly people in the borough in an attempt to get bank card details over the telephone.
The first victim, a man in his 70s from Hersham, received a phone call from a man claiming to be a police officer in Birmingham on Monday, August 4, at about 7pm.
The caller told the elderly victim that one of his bank cards had been compromised and asked him for details of the card and the Pin.
The victim refused to give any personal information and ended the call.
On the same day, at about 7.35pm, a resident in Brooklands Road, Weybridge, also received a call from a man claiming to be a police officer.
The man told the victim there had been illegal transactions on her bank cards and asked her to provide more details.
But the victim was suspicious about whether the call was genuine, refused to give any information and ended the call.
Surrey Police said they were investigating a series of offences across the county where fraudsters obtain bank details, cards and cash by carrying out bogus telephone calls and hiring couriers to pick up bank cards from their victims.
In many offences, victims are told their bank cards have been used by someone who is in custody and the fraudsters ask the victim to call their bank to cancel the card, saying they will send a courier to collect the card.
As the victim calls their bank, the fraudster stays on the line and obtains their details before sending a courier to their home to collect the card.
PC Goffe said: "The callers will often sound very genuine and the version of events they describe might seem plausible but I would like stress that these requests are not genuine and that no police officer or bank would operate in this manner and would never require a customer to confirm their pin details or withdraw money over the phone."
Anyone with information on the scams should call Surrey Police on 101, quoting reference 45140065308 for the Hersham incident and 45140065307 for the Weybridge incident.