The Home Secretary, David Blunkett, said yesterday he was prepared to look at ways of preventing the media releasing the names of celebrities accused of sex offences.
Speaking on Radio 4's Today programme, Mr Blunkett played down suggestions that the law might be changed to give defendants charged with sex crimes the same right of anonymity as complainants prior to their conviction.
However, he said he would like to forge an agreement restricting the reporting of cases like that of John Leslie.
The former This Morning and Blue Peter presenter was charged with two counts of indecent assault earlier this year, which were dramatically dropped last week by the Crown Prosecution Service.
Commenting on the case, Mr Blunkett revealed that he had been alarmed by the extent of the media coverage long before Mr Leslie was ever arrested or charged.
"[John Leslie's name] was found out by the media and we have to ask the question how do we stop the media reporting something they are determined to report?"
Referring to the wider issue of anonymity for the accused in sex offence cases, he said: "These are difficult issues which Parliament should debate openly.
"We didn't think that the case had been made any more than for any other heinous crimes, not least murder. We felt that what we should do is sit down with the media and try to work out whether we could strengthen what already existed."
Mr Blunkett also rejected suggestions that he was unhappy at the decision of the Lord Chief Justice, Lord Woolf, 70, to delay his retirement.
"I am always happy to do business with Lord Woolf," said Mr Blunkett. "He has to bat his corner for what he believes to be his remit."