A man in his 90s was tricked into going to his bank with a view to withdrawing all his money by a bogus telephone caller.
Three other people, including a woman also in her 90s, have received similar calls, all in Fakenham in the last couple of days.
The callers pretended to be police officers and said someone had tried to fraudulently access the bank accounts of their victims.
Superintendent Stuart Gunn said: “I urge all members of the public to remain vigilant against these scams and esepcially ask anyone with elderly relatives and neighbours to inform them about the tactics these conmen employ. “
Bank staff alerted police when the elderly victim of one of the calls arrived to withdraw cash.
Supt Gunn said people should never give details of their PIN to anyone and police would not ask for bank card or bank account details or ask to come and collect those items.
He also urged caution over making an immediate call from the same number to the bank to check the legitimacy of a call received. Fraudsters are sometimes still on the line.
Two bogus calls were reported on Wednesday and two this morning.