Bogus callers claiming to be from BT have been targeting people in Waverley by threatening to disconnect their telephone lines and demanding money.
Surrey Police said there had been several incidents in which homeowners were told they had an outstanding bill.
The callers claim they will cut off the line temporarily to prove they are from BT, but stay on the line with mute on.
The residents then test the line unsuccessfully, after which the callers call back to demand bank details.
During the scam, the caller tells residents they will face a £118 reconnection bill if they do not pay immediately.
Pc John Robini said: "I would urge householders never to give out bank details or other personal information over the phone whatever the reason behind the request.
"Companies, such as BT, would never operate in this way.
"They would write to customers if they needed further financial information."