As many as six million people may have paid incorrect amounts of tax and national insurance through the PAYE system.

According to figures from the Treasury, some £2 billion has been underpaid due to errors in the way that HM Revenue and Customs' PAYE calculation system works.

This has resulted in about 1.4 million taxpayers owing some £1,500 each for underpayments over the past two years.

The money will be reclaimed through an amendment of their PAYE tax codes which will be introduced next year rather than through a single demand.

But there have been a series of miscalculations affecting people who have overpaid their income tax and national insurance contributions too. As much as £1.8 billion in overpayments may have been collected from 4.3 million people.

They will be entitled to a tax refund and a cheque in the post. Rebates could be as much as £400.

The errors came to light following a 'reconciliation' review of the PAYE system which found widespread underpayments by employers.

But figures indicate that the total number of people affected could hit 18 million because there are still open historic cases of under- and overpayment for the years pre-dating March 2008.

Those taxpayers affected by errors in the past two years will be receiving letters between now and Christmas informing them of the scale of the miscalculations.

Employees who have moved jobs or accepted company cars or cash benefits from their employers are more likely to have been caught up in the system's inability to cope with modern employment practices.

Many of the problems arose and were identified because, where HMRC once conducted manual checks to ensure that the amounts deducted in tax and national insurance tallied with the information on the tax authority's records, the process has now been computerised.

Treasury Minister, David Gauke said that, given the current economic climate, moves would have to be made to recoup the lost tax take and that the government was not in a position to "wave goodbye" to money owing.

Some taxpayers may find that they have both under- and overpaid their tax, with the two amounts more or less cancelling each other out.

In certain cases, HMRC said that it would consider waiving demands for extra money if taxpayers could demonstrate they had provided all the information necessary to calculate their tax liabilities accurately.

Mr Gauke said that the government intends to move sensitively and cautiously on the issue: "At the moment we have said that those who owe more than £2,000 - those who are obviously in the most difficult position - we're reviewing exactly how we're going to do that.

"For those who owe less than that we will be seeking to recover that over the course of the 2011-12 tax year through tax codes."

A HMRC spokesman added: "The overwhelming majority of PAYE cases - over 40 million - are right, so most people have paid the right amount of tax.

 "But for a variety of reasons in some cases there will be a discrepancy. The government accepts that the way we go about deducting tax at source needs to be much more accurate and the introduction of the NPS [computer system] paves the way for a real time system which in turn boosts accuracy.

"The roots of this are in the fact that PAYE came in during the Second World War in 1944, at a time when many people stayed with the same employer during the whole of their working lives. It's not like that anymore.

"We have to reflect that and have new systems. Because circumstances change during the year there will always be a minority who have paid either too much or too little. This year, and going forward, the new IT system will mean more people paying exactly the right tax at the right time than ever before."