More people are receiving demands for back-tax amid warnings from the Government that they have little chance of escaping payment.
Treasury minister David Gauke said those affected by a HM Revenue & Customs blunder should not "build up their hopes" that appeals will succeed.
The intervention came after HMRC started sending out nearly six million letters to individuals who paid too much or too little income tax.
Around 4.3 million people are due a rebate, but some 1.4 million will have to hand over an average of £1,428 each.
Experts said people hit with an unexpected tax demand may be able to refuse to pay up as HMRC could have exceeded its own time limits in which to ask for the money.
Under tax rules HMRC must issue demands for underpaid tax within 12 months of the end of the tax year in which it became aware that people had underpaid. But if people provided all the information needed to get their tax code right, HMRC should have used these details within 12 months of the end of the tax year in which it was received to claw back the extra money. If HMRC failed to do this, taxpayers can ask for an Extra Statutory Concession, also known as an ESC A19.
The latest round of errors date back to April 2008, meaning anyone who alerted HMRC to changes in their circumstances that affected their tax code before the start of the new tax year in April 2009 may be able to cite this clause.
But Mr Gauke said that although the Government is keen that "everybody who is in a position of having underpaid their tax is treated sympathetically", experience had shown that "very few" appeals against payment demands succeeded.
He added: "Some do and we do not deny that, and we are looking to see how that process can operate. But I don't want people to build up their hopes too much and think that there is a sort of panacea. The fact is most of these appeals are unsuccessful."
Asked specifically about the ESC A19 concession, Mr Gauke replied: "There will be some cases where it will be applicable here but as I say the experience that HMRC have had is that it will only apply in a very small minority of cases, and almost certainly it will not apply at all for anything relating to the 2009/10 tax year, because it is very recent."