Whitehall mandarin Alan Budd discovered there was a fax and an email from Mr Blunkett’s office discussing the case and the Home Secretary told Prime Minister Tony Blair he would resign forthwith.
Mr Blunkett insisted he had no personal recollection of dealing with the case but accepted full responsibility.
Mrs Quinn is married to Kilkenny-born Stephen Quinn, managing director of Vogue magazine.
Mr Blunkett’s resignation became inevitable after Labour colleagues made clear they were withdrawing their support for him.
Colleagues said his bitter paternity battle with Mrs Quinn over her son was an embarrassment to the British government, no matter how strongly they sympathised with him.
It was the granting of Indefinite Leave to Remain (ILR) to nanny Leoncia Casalme which provided the trigger for Mr Blunkett’s decision after he was accused of taking up her case.
At first the Home Office insisted Mr Blunkett had only checked her application for factual errors. Then it emerged she was told it might take a year - but 19 days later it was granted.
In a statement Mr Blunkett said: “When the issue of the application for ILR 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.
“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 delay) of which I was always aware but did not remember holding a copy. I have no recollection of dealing with this.
“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 I have tendered my resignation.”