The con artists, claiming to be from HM Revenue & Customs (HMRC) are tricking people into paying non-existent debts using iTunes gift cards.
Action Fraud, the National Fraud and Cyber Crime Reporting Centre, said it had received hundreds of calls in the past month related to the con.
The scammers are using a variety of methods to contact victims, including voicemails, text messages and direct phone calls.
In each instance, victims are told that they own an outstanding debt to HMRC and are asked to make a payment using iTunes gift card voucher codes.
'It's been a blast': pub legend Malcolm the Fish Man retires
Corby man given suspended sentence after showing 'gun' to group in pub
Kettering NHS worker scoops £1m lottery jackpot just before finishing cancer treatment
PICTURES: Here are six abandoned but adorable dogs looking for a forever home this week in Northamptonshire - including one big lad with a 'shoe fetish' 🐶
Meet 105-year-old Marjorie - who must be Kettering's oldest property landlady
In several cases those targeted have handed over thousands of pounds after being taken in by the fraud. One victim handed over codes worth £15,000 after a cold caller convinced them they owed the sum to the Government.
The scammers are demanding payment in iTunes gift cards because they can be easily redeemed and sold on. The scammers don’t need the physical card to redeem the value and instead get victims to read out the serial code on the back over the phone.
The fraudsters are contacting victims in three ways: by voicemail, text message or spoofed calls. When victims contact the number left in the messages they are told either that HMRC is building a case against them for an outstanding debt or that a warrant has be issued for their arrest. They are then convinced that to avoid this they must make the payment using the voucher codes.
In the wake of the new scam Action Fraud has emphasised that HMRC will never use texts to tell you about a tax rebate or penalty or ever ask for payment in this way.
It also warned that phone numbers can easily be spoofed and that if you are in any doubt about the legitimacy of a call you should hang up immediately.