David Blunkett has won the first round of a High Court battle with his ex-lover over access to her son.
Mr Blunkett pictured with Mrs Quinn at a function last year
Mr Justice Ryder rejected a plea for the paternity hearing to be postponed until April on the grounds that Kimberly Quinn's health was at risk.
He accepted the argument that the home secretary's relationship with the child he says he fathered could be damaged if there is a delay.
Mr Blunkett said he was "relieved" he could continue his bid to gain access.
The home secretary appeared in person at London's High Court on Thursday having lodged an application on 11 November.
Mrs Quinn, 44, was unable to attend the hearing in London because she was in hospital getting treatment for complications with her pregnancy, the judge told an open court session on Friday.
She claimed at a private hearing that taking part in the proceedings would put her own health and that of her unborn second child at risk, as well as affecting the welfare of her two-year-old son.
But the judge rejected claims that she would not get a fair hearing unless the case was adjourned until next April.
He dismissed an appeal by Mrs Quinn against a lower court's decision not to adjourn the proceedings.
The judge named the child as A and said future hearings would be held in private.
In a statement, Mr Justice Ryder said: "I have come to the clear conclusion that having regard to the quantity of material that is in the public domain, some of it even in the most responsible commentaries wholly inaccurate, it is right to give this judgment in public."
He said that if the court remained silent, it would promote further speculation and adverse comment that will damage both the interests of those involved and the family justice system.
Mr Ryder accepted the case should not be postponed
In a statement, Mr Blunkett said: "I'm naturally relieved at today's judgment so I can continue my attempts to gain access to my son.
"I have never wanted anything about my private life and (A's) paternity to be in the public domain and would never have gone to the courts if there were another way of getting informal access to him.
"I still hope this may be possible as I have not seen
(A) since August.
"As forthcoming court hearings will be held in private, I will not be commenting further on these personal matters and I hope everyone concerned for (A's) welfare will do the same."
The judge said there had been "inaccurate speculation" about the case and that Mr Blunkett had never sought a residence order or scientific paternity tests.
In his application, Mr Blunkett was described as the father of the child and Mrs Quinn as the mother.
Mrs Quinn did not accept that Mr Blunkett was the father and if she was right, his application for a parental responsibility order would be fatally flawed, said the judge.
Mr Ryder upheld a district court judge's earlier findings that it was in the child's best interests to have his parentage determined at the earliest opportunity by a court ordering scientific tests.
Mr Blunkett's official spokesman said outside court that the first hearing in the case took place on 23 November.
"The only reason there's a judgment today is that Kimberly Quinn made an application in a private hearing last week.
"The reason it's being heard in public is because the judge decided there were too many myths in the public domain," he said.
Asked to comment on the case, Tony Blair's official spokesman said: "David Blunkett continues to do the job he has to do for the government and the country."
Asked if he regarded Mr Blunkett's legal battle as a purely personal matter, the spokesman replied: "Correct."
These comments were backed up by Conservative Shadow Chief Secretary to the Treasury George Osborne who said: "What goes on his private life shouldn't affect his ability to do his job".