Two incidents occurred in the Rosegrove and Coal Clough Lane area where the victims, in their 70s and 80s, had their cards stolen by a man calling at their home who was claiming to be a police officer.
A spokesman for Burnley and Padiham Police has now appealed for people to be vigilant saying: "Please do not allow anyone into your property if you aren’t satisfied with their identity.
"A genuine police officer will be happy to provide the correct identification.
"If you have elderly neighbours or relatives please pass this message on and be extra vigilant."
Police are now conducting inquiries to identify the culprit.