The woman is said to have been contacted on Tuesday March, 21 by the fraudsters who said she had an unpaid tax bill dating back to 2016.
Police say the con-artists then told the woman they had a warrant for the woman's arrest and asked her to buy Itunes gift cards to pay her 'fine'.
The scammers then asked for the serial numbers to the cards and successfully stole Â£1,400 from the woman.
Investigating officers are now warning that the con-artists have been prolific across the whole of Lancashire and are asking residents to warn their elderly or vulnerable friends and relatives about the scam.
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A spokesman for Blackpool police said: "We have been recently made aware of this scam operating across our area.
"We have received a few reports, but believe we should be receiving more reports of this scam then we actually are.
"This lady was unfortunately the victim of the fraud and we are now asking for residents to make sure elderly and vulnerable relatives are aware of this scam."
Action Fraud said the con-artists operated in a number of ways using voicemails, texts, emails direct cold calls.
Another 87 year old victim recently told the BBC he was phoned by fraudsters who claimed to be from HMRC stating there was an arrest warrant out in his name. They told him it would be cancelled if he bought Â£500 in iTunes gift cards at Tesco.
The man bought the cards and gave them the serial numbers. But when they asked for a further Â£1,300 in vouchers, he became suspicious and hung up.
A spokesman for the HMRC said in a statement: "HMRC is aware of bogus phone call scams, where the caller claims to be from HMRC. The fraudster may encourage you to give personal and financial information in exchange for a tax refund or say that HMRC is filing a lawsuit against you and that you must make an immediate payment
"This scam has been widely reported, and appears to be targeting elderly and vulnerable people.
"If you can’t verify the identity of the caller, we recommend that you don’t speak to them.
"If you’ve been a victim of the scam and suffered a financial loss you can report it to Action Fraud."
Methods fraudsters use:
Spoofed calls: Fraudsters cold call victims using a spoofed number and convince them that they owe unpaid tax to HMRC.
Voicemails: Fraudsters leave victims automated voicemails saying that they owe HMRC unpaid taxes. When victims call back on the number provided, they are told that there is a warrant out in their name and if they don’t pay, the police will arrest them
Text messages: They may also use text messages that ask victims to urgently call back on the number provided. When victims call back, they are told that there is a case being built against them for an outstanding debt and they must pay immediately.
How to protect yourself:
HMRC will never use texts to tell you about a tax rebate or penalty or ever ask for payment in this way.
Telephone numbers and text messages can easily be spoofed. You should never trust the number you see on your telephones display.
If you receive a suspicious cold call, end it immediately.