Mr Blunkett predicted he would be cleared of fast-tracking the visa application of his former lover’s nanny.
But he said he still had to go to protect the integrity of the prime minister.
“The thousands of people who wrote to me and rang me and emailed me believed in my honesty and integrity,” he said.
“And that, above all, is critical not just to me but also for the integrity of Tony Blair who has backed me to the hilt.”
Mr Blunkett had been under mounting pressure over claims that he helped his ex-lover Kimberly Quinn’s Filipina nanny Leoncia Casalme get leave to stay in Britain and get visas for foreign trips.
He has consistently denied any wrongdoing but fell on his sword yesterday after Sir Alan Budd presented him with new evidence.
In his statement, Mr Blunkett said: “When the issue of the application for ILR (indefinite leave to remain in the UK) for Ms Casalme emerged on November 28, I immediately asked for an inquiry to be set up.
“Sir Alan Budd has undertaken that inquiry over the last two weeks.
“The key issue has always been whether I used my public office for private benefit.
“Since these issues were first raised, I have always given my honest recollection of the facts, on the record as I remembered them.
“At that time, and subsequently, I said that the issue of Ms Casalme’s application was not taken up by my office beyond it being read to me initially.
“These statements have been based on the recollections of myself and the officials in my office at the time.
“Yesterday, Sir Alan Budd told me there had indeed been a fax and an exchange of emails between my office and the Immigration and Nationality Directorate - not based on the application form as originally alleged but on the subsequent letter (informing her of a possible 12 month delay) of which I was always aware but did not remember holding a copy. I have no recollection of dealing with this in any way.
“Given I have no recollection of issuing instructions to deal with the application, but only to continuing the elimination of the backlog in general, the easy thing would be to hide behind my officials.
“I will not do such a thing. In no way is my office or any individual within the department to blame for what happened.”
Mr Blunkett said his problems would never have arisen if he had not insisted on maintaining contact with Mrs Quinn’s son, who the Home Secretary believes to be his child. Mrs Quinn disputes this and the couple are locked in a legal battle.
Mr Blunkett, a divorced father of two grown-up sons, said: “I could not live with myself or believe I had done the best for him in the long-term if I had abandoned my relationship with him.”