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In his resignation statement, Mr Blunkett insisted he had done nothing wrong, but said questions about his honesty had damaged the government.
"I have always been honest about my recollection of events," he said. "But any perception of this application being speeded up requires me to take responsibility."
Mr Blunkett said he had not been aware of the contents of an email which had used the phrase "no favours but slightly quicker" about processing the application.
The email was discovered during an official inquiry into the allegations against Mr Blunkett, led by Sir Alan Budd and due to be published later this month.
The resignation is a serious blow to Tony Blair's Labour government, coming as it does just a few months before a general election.
Mr Blunkett's troubles began in August, when tabloid newspaper The News of the World revealed he was having an affair with a married woman.
She was later named as Kimberly Quinn, the American publisher of The Spectator magazine.
The affair became public after it had ended, and Mr Blunkett has now begun legal proceedings to gain access to Mrs Quinn's two-year-old son William, who he claims is his.
He won the first round of his High Court battle two weeks ago.
He is also trying to establish whether he is the father of the baby Mrs Quinn is expecting early next year.
Today the prime minister, who has backed the home secretary throughout, described Mr Blunkett as a force for good in British politics who had "left government with his integrity intact".
Mr Blunkett's Tory shadow, David Davis, said Mr Blunkett has done the "honourable thing" in resigning.
"I feel sorry for him," he said. "He is a tough opponent and a remarkable man. It is a sad day for him."
Mr Blunkett became Home Secretary in 2001, a few months before the September 11 attacks in New York.
During his term in office he has pushed through many tough and sometimes controversial new policies on anti-terrorism, asylum seekers and anti-social behaviour.
David Blunkett was replaced as home secretary by the Education Secretary, Charles Clarke.
The Budd report was published in full on 21 December. Sir Alan found a "chain of events" linking David Blunkett to the faster-than-average issuing of a visa to Mrs Quinn's nanny.
But he was unable to say whether Mr Blunkett had sought special help for the nanny or had just been highlighting an example of the poor performance of the immigration directorate.
Kimberly Quinn gave birth to a baby boy in February 2005. A DNA test established that Mr Blunkett was not the father.
His battle for access to Mrs Quinn's eldest son William continues.
The furore surrounding the home secretary's love affair and subsequent resignation has been the subject of two highly satirical stage plays and a TV lampoon, A Very Social Secretary, screened in October 2005.
Mr Blunkett returned to the Cabinet less than five months after he resigned, becoming Work and Pensions Secretary following Labour's 2005 election victory.
However, he was again forced to resign in November 2005 after breaking the ministerial code of conduct over paid work he took while he was out of Cabinet.
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