The Sun newspaper said yesterday that it would not appeal against an injunction won by the Attorney-General preventing it from naming the 17- year-old.
But the Cabinet minister said he was frustrated that he was prevented in law from going public about his predicament.
In an interview with the Mirror today, he said he had prepared a statement before taking his son to the police but then found he was legally bound to remain anonymous after the youth was arrested.
"I want to talk about this in public and reveal my identity but I have been told I can't. Lawyers have said I haven't got any choice. I'm not in any doubt about that," he said.
"That is obviously very frustrating because I am not the sort of person who normally avoids confronting issues like this publicly." He added that he had asked that his son be treated no differently from anyone else.
He also said that the arrest of the reporter who broke the story, Dawn Alford, was nothing to do with him. "They [the police] make their own decisions and that's always the way the police operate. It would be outrageous if politicians were to interfere in who was arrested."
On Tuesday evening, Mr Justice Moses granted the Attorney-General, John Morris QC, an injunction banning the Sun from publishing the name of the minister's son.
He ruled that while the Children and Young Persons Act 1933 protecting a juvenile's identity in court proceedings did not apply, under the law of contempt publication could prejudice a trial, add to the burden of any sentence and wrongly stop the trial judge banning publication of identity during the case.
Dan Te, a media specialist at solicitors Lovell White Durrant, said the ruling "strained" the law of contempt. Walter Greenwood, editor of Essential Law for Journalists, praised the integrity of the Attorney- General, but said the injunction "gave the appearance of double standards".
Some observers saw the Sun's failed attempt to publish the name as a ploy to draw attention from the rival Mirror, which ran the story before Christmas. Tim Ross, the legal spokesman for the Sun, said: "We felt we had good legal grounds to name the minister but we have decided that arguments on both sides were thorough and the judge took time to consider his judgement."
Paul Cavadino, principal officer of the National Association for the Care and Resettlement of Offenders, defended the injunction, adding: "It is important to remember that the anonymity rule exists to protect juvenile defendants, not to protect their parents from embarrassment.".
The Tory spokesman on home affairs, Sir Brian Mawhinney, said the case had become a "slow torture process" for the cabinet minister's family.
Meanwhile, Acting Metropolitan Police Commissioner Sir Brian Hayes has rejected claims of political pressure. Ms Alford's arrest was part of normal police practice and had not been ordered by the Crown Prosecution Service, although they had been consulted as was standard in such cases.Reuse content