Up to 13,000 civil servants are said to have been affected by the fraud, after criminals used the internet site to steal their identities.
The e-portal for tax credit claims, used by around 500,000 people a year, was shut down on December 2, as ministers revealed that HM Revenue and Customs (HMRC) had uncovered attempted frauds linked to the site.
An "in-depth investigation" was launched into the apparent false use of "a number" of Department of Work and Pensions (DWP) staff identities in fraudulent claims for the credits.
But Liberal Democrat work and pensions spokesman David Laws accused ministers today of seeking to "hush up" the scale of the problem.
Whistle-blowers inside the DWP and HMRC had told him that thousands of staff, particularly from the former Benefits Agency, may be affected, as their payroll system may have been accessed by criminals.
The Public and Commercial Services union (PCS) said that 13,000 staff are involved in centres in London, Glasgow, Pembroke Dock in Wales and Makerfield in Lancashire.
Credits of as much as £1,000 a year appear to have been diverted into fraudsters' bank accounts, said PCS spokesman Alex Flynn.
"Some people have had shadow bank accounts set up and their money diverted to that account. Other people have had their accounts hijacked," he said.
"What we are asking is that nobody is left out of pocket, especially as we are in the festive season."
The PCS believes that successive rounds of job cuts may be partly to blame, as staff operating the credits have become too stretched to carry out adequate checks, he said.
Mr Laws claimed that HMRC may have known about the internet fraud problem for as long as two years and alleged that basic checks - such as demanding a birth certificate to be sent in as proof of identity - were not put in place to stop it.
He wrote to the Auditor General Sir John Bourn today to demand an investigation by the National Audit Office.
The alleged frauds are the latest problem to afflict Chancellor Gordon Brown's flagship tax credit system, after a series of computer glitches and anger over claimants being required to pay back overpaid credits.
Mr Laws claimed that staff hit by the problem have been given "very little help", and are simply told to call a tax credit helpline.
And he said that the problem has spread to include telephone claims, with criminals redirecting tax credit payments into other bank accounts.
HMRC staff have told the Liberal Democrats that people are fraudulently calling in on the tax credits helpline and changing addresses, and then following up further by changing bank account details, said Mr Laws.
But the HMRC said it had no evidence of any fraud relating to telephone claims.
And the DWP insisted it was confident the problem was limited to a "specific group" of staff and that it was taking measures to support them during the investigation.
Mr Laws said the "accident-prone" tax credit system has become a "fraudsters' dream".
"It now seems that we are losing many millions of pounds of taxpayers' money to organised fraud," he said.
"Government action to stop the fraud has simply been too little and too late.
"The tax credits system has not had enough checks in place, and it has turned out to be a fraudsters' dream. Now millions of pounds may have been lost, and thousands of genuine claimants have had their tax credit claims abused and their money stolen.
"I have asked the National Audit Office to mount an urgent investigation into this tax credit fraud, and I will be pressing for a statement in the House of Commons from the Chancellor.
"Hoping the problem will go away and hushing it up is a betrayal of taxpayers and all the honest, genuine claimants that are falling victim to this scam.
"The extent of this fraud could be immense, and people need to be warned."
A spokesman for HM Revenue & Customs said: "We take any suggestion of fraud against our systems extremely seriously and are conducting a criminal investigation into this case with DWP. Whilst the investigation is ongoing, we can't comment in detail.
"When fraud happens, we move quickly to stop any further payments being made to the fraudster, prosecute those responsible and get the legitimate claim back on track.
"We always investigate allegations of fraud and we can and do prosecute fraudsters."
The spokesman added: "We have no evidence of any specific attempt to defraud the tax credits telephone service. We always thoroughly investigate any suggestion of fraud and we can and do prosecute fraudsters."
A spokeswoman for the DWP said: "We are taking this issue very seriously. A criminal investigation is now under way and we are working hard with HMRC to resolve the matter.
"Our staff are understandably concerned but we are confident from the information we have that the issue is limited to a specific group.
"We have kept staff up to date by issuing bulletins and ensuring line managers in the regions affected have been briefed.
"Alongside the tax credit helpline, we have set up a telephone service for line managers to call if they need further information. We are also liaising with our unions so they understand the position."
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