As many as 1.4million people are set to receive a letter from HMRC claiming that they have underpaid tax over the past two years, owing an average of £1,500 each.

About £2bn was underpaid through the PAYE (pay as you earn) system over the past two financial years, with 1.4m people now set to receive demands for the underpaid sum from Her Majesty’s Customs and Revenue.

In addition, around 4.3m have been found to have overpaid tax over the same period, resulting in tax refunds totalling £1.8bn, or £418 on average per person.

Treasury minister David Gauke said that in the current financial climate, the government was not in a position to "just wave goodbye" to the money owed and claimed that the previous systems for PAYE were struggling to cope with modern working patterns.

A new computer system introduced by HMRC in 2009 has allowed more discrepancies to be identified.

As a result millions of letters will be sent to taxpayers across the UK informing them of errors in their contributions. The first 45,000 are expected to arrive on Tuesday, with 30,000 informing recipients they are due a rebate of on average £418.

The remaining 15,000 letters will tell taxpayers they have underpaid and will have their tax code altered next year to recoup the money.

It is thought that some individuals may face both underpayments and overpayments, which could cancel each another out.