David Blunkett has quit as home secretary after an e-mail emerged showing a visa application for his ex-lover's nanny had been fast-tracked.
Mr Blunkett says he has done nothing wrong
The e-mail had said "no favours but slightly quicker". Mr Blunkett said he had not been aware of its contents and insisted he had done nothing wrong.
But he said questions about his honesty had damaged the government.
Downing Street has named education secretary Charles Clarke as Mr Blunkett's replacement.
Mr Clarke said he was "exhilarated" by the challenge ahead but added: "There will be continuity between David's approach and mine."
Cabinet Office minister Ruth Kelly will replace Mr Clarke as education secretary.
Tony Blair described Mr Blunkett as a force for good in British politics who had "left government with his integrity intact".
Sir Alan Budd's inquiry into the nanny allegations established there had been an exchange of e-mails about the visa application between Mr Blunkett's office and immigration officials.
Mr Blunkett said: "I have always been honest about my recollection of events.
"But any perception of this application being speeded up requires me to take responsibility.
"That is why with enormous regret I have tendered my resignation to the prime minister today."
Former civil servant Sir Alan had been due to unveil his findings before the Christmas break.
Conservative shadow home secretary David Davis paid tribute to Mr Blunkett saying he was a "tough opponent".
But Mr Davis said he had quit because he realised the Budd inquiry would "find against him".
Mr Davis added: "This sort of misuse of office is not allowed in British politics."
In an emotional interview with BBC Political Editor Andrew Marr, Mr Blunkett said: "I did not in August initiate the terrible trauma of my relationship (with ex-lover Kimberly Quinn) coming to the fore.
"I did not in late November start the plethora of linking my private life with public events again.
"I am mortified that that was done and I am very sorry. I'm not even angry, I'm just terribly hurt and I want people to know that in my public life I have always tried to help people.
"I have never tried to fiddle my role as leader of the city of Sheffield, as an MP or as a minister."
Mr Blunkett suggested he had been willing to sacrifice his political career to pursue his paternity claim to Mrs Quinn's son.
"He will want to know not just that his father actually cared enough about him to sacrifice his career, but he will want to know, I hope, that his mother has some regret."
The prime minister has stood by Mr Blunkett throughout the row.
But the home secretary's position became more uncertain after he criticised a string of Cabinet colleagues in a new biography.
A copy of a new biography of Mr Blunkett - containing attacks on colleagues - was hurled across the Commons chamber by government Chief Whip Hilary Armstrong.
Her gesture was widely interpreted as expressing her frustration at the continuing controversy enveloping the then home secretary.
Mr Blunkett said Mr Blair had "backed me to the hilt," adding: "I have built my reputation on honesty, I have sometimes been too honest."
Liberal Democrat home affairs spokesman Mark Oaten said Mr Blunkett had done the right thing.