Home Office Minister Beverley Hughes is under renewed pressure to quit after a second civil servant was suspended for raising immigration concerns.
Hughes will not resign or be sacked, says Mr Blunkett
The British consul official in Bucharest faces disciplinary action after alleging immigrants are allowed into the UK without checks.
James Cameron e-mailed his concerns to shadow home secretary David Davis, who accused the government of a cover-up.
Ms Hughes says she will not quit or be forced out of office.
Mr Davis said Mr Cameron had claimed checks waived by Sheffield immigration officials, which led to the suspension of whistleblower Steve Moxon, were the "tip of the iceberg".
The latest allegations came after Tony Blair's official spokesman said the prime minister continued to have confidence in immigration minister Ms Hughes.
She said she was "appalled by what David Davis has done", arguing that he should have raised his concerns earlier.
Mr Davis said: "The government's attempts to cover up information this man sent me knows no bounds.
"After smearing one civil servant, they now suspend a British Consul for doing what he feels is his public duty, namely telling Parliament what Beverley Hughes left out of her account of the whole immigration system.
"It beggars belief and goes to the heart of what this government truly stands for."
A Foreign Office spokesman said: "A British member of staff in the embassy in Bucharest is facing disciplinary procedures.
"We don't comment on individual cases but there is an ongoing investigation."
Last week the Sutton Report found a decision to waive checks in Sheffield on eastern Europeans seeking to come to Britain to set up businesses had been taken by junior staff without ministers' approval.
Mr Davis said the suspended entry case manager, Mr Cameron, from Glasgow, had told him the system applied not just to people from nations joining the EU in May, but also to those on the next list of accession countries, including Bulgaria and Romania.
Mr Cameron's e-mail to the Tories continued: "When entry clearance officers write to Sheffield and state clearly that the application is being supported with forged and counterfeit documents the letters are ignored and the ECAA applications are still being issued."
Davis: Accused ministers of cover-up
But a spokesman for the home secretary said Mr Davis should have raised his concerns when the e-mail was sent on 8 March.
"The fact he has chosen to release it now is a blatant piece of news
management and spin by David Davis," he said.
Ms Hughes faces resignation calls after reports claiming she approved the fast tracking of immigration claims, but she said she would not be quitting.
She told BBC News 24 she was appalled Mr Davis had kept the e-mail "secret", insisting people did not get into the UK on forged documents, although "clearly some people try to".
She said a complete overhaul of the immigration system, initiated on the back of the Sutton inquiry, plus an investigation by the National Criminal Intelligence Service, would also consider Mr Davis's allegations.
She accused him of trying to "keep this story going and to do more damage to the government".
Earlier Mr Blunkett supported Ms Hughes and turned his fire on the "right-wing" press.
"Let me absolutely clear: Beverley Hughes is not going, she's not resigning, she's not going to be sacked."
The home secretary later published a list of similar schemes used since 1988 to waive some checks for people already living in Britain.
Mr Blunkett said the policy authorised by Ms Hughes was different from the Sheffield cases - which were done without ministers' knowledge - because it only covered people already in Britain.
But his defence was rejected by Tory leader Michael Howard, who renewed Tory calls for her resignation, claiming she had "misled" the Commons.
The issue is set to be the centrepiece of an opposition-led debate on immigration on Tuesday.
A memo from senior managers at the Immigration and Nationality Directorate in Croydon, leaked to the Sunday Times, stated a backlog of applications from people who had been in the country for more than three months should be cleared "as quickly as possible", with ministerial backing.