The caller is trying to sell a call-blocking service, which they are advertising for a one off fee of £20-£22. The caller has also used terminology such as "your call blocking service is coming to an end."
The number used by the scammers has been reported as 02753189849.
A check on the national scam sites has shown a number of victims to this scam. Reports show that the caller has been identifying themselves 'Shirley' and calling from the 'Telephone Preference Service' or the 'Telephone Management Company'.
A post on Scarborough Police's Facebook page said: "Please do not be drawn in to buying services from callers such as these. Please do not give out your bank details over the phone.
"You can purchase products which provide call blockers, call identity products and call screening facilities. Don't find yourself being pressured in to buying something."
"If you want to speak to someone in relation to this or other scam/fraud incidents, please feel free to call in to Scarborough Police Station (8am - 8pm) or call 101 to speak to your local Neighbourhood Policing Team officer."