By effectively disowning the super-injunction he sought more than three years ago, Andrew Marr has provided a useful fillip to those who have been arguing against the increasing use of these so-called "gagging orders".

In coming clean in yesterday's Daily Mail, Mr Marr did not go so far as to express regret for seeking the order. The BBC presenter – and one-time editor of The Independent – said the story was "nobody else's business" and that he had had his wife and children to think about, as well as the child he thought (wrongly, as it turned out according to a DNA test) he had fathered with another woman. But he fears gagging orders are running out of control and feels "uneasy" about what he did.

Was he wrong to seek a super-injunction? The argument about protecting the child he believed he had fathered was a red herring since the child's identity is still not known. Why, then, should he have been granted a gagging order? Mr Marr is a public figure who puts politicians under the microscope. He had also written a piece saying that Parliament, not the judges, should develop a privacy law.

So the campaign by Ian Hislop, editor of Private Eye, to undo his super-injunction seems entirely justifiable. My guess is that most people will probably agree it should never have been granted – and that Mr Marr in his heart probably does, too. He had done something that he regretted, and regretted it at least partly because he knew it was wrong. He should not have gone to the law to conceal this and the law should not have allowed it.

There are thought to be 30 super-injunctions in force but we do not know because the nature of a super-injunction is that its very existence cannot be reported. Only last week, Mr Justice Eady delivered a contra mundum injunction which prohibits the media in every jurisdiction in the world, and until the end of time, from reporting the allegations of a woman against a well-known household name. Like many journalists, I know his identity, but would be hauled off to the Tower of London were I to reveal it.

Several of these super-injunctions concern footballers whose sexual adventures may seem of very little relevance or interest to any of us. But I know of one for a public figure whose gigantic failures cost the public hundreds of millions of pounds.

There are other super-injunctions in which the sexual element is of secondary importance to serious alleged wrongdoing or, occasionally, entirely absent. The oil-trading firm Trafigura, which had denied being responsible for a toxic-waste dumping scandal in Africa, was granted a super-injunction in 2009 that was only lifted after a Labour MP asked a question in the Commons.

Judges – over the years Mr Justice Eady has often been at the forefront – are choosing to emphasise the rights of privacy enshrined in Article 8 of the European Convention on Human Rights, over Article 10, which upholds the right of free expression. Last week David Cameron said he was "uneasy" about the spread of super-injunctions by which judges are introducing a privacy law, sometimes in secret.

Is it too much to hope that Mr Marr's dignified confession, coming so soon after Mr Cameron's intervention, might mark a kind of sea-change? Parliament must take this matter out of the hands of unelected judges, and sanction a more balanced, home-grown privacy law which does not allow rich celebrities and public men – it is nearly always men – to muzzle the media.