One of the more remarkable features of the "war on Leveson" waged by leading British papers has been their willingness to appeal to the European Convention on Human Rights. In the cases of several newspaper groups this is the most flagrant hypocrisy. They have consistently accused the Court of Human Rights of ignoring the will of a democratically elected parliament, but this is precisely what they want the court to do now in relation to the Leveson recommendations.

Newspapers have, on many occasions, argued that the judge’s proposals are in breach of their human rights. At least four legal opinions on this have been commissioned and though none has been published some have leaked. One, obtained from three QCs, concerned the compatibility of exemplary damages with Article 10. Then there was an opinion on "apologies" and related matters. Most recently, there was an opinion from Antony White QC which, according to the Times, said that the costs incentives for joining a new self-regulator were "arguably incompatible" with Articles 6 and 10 of the Convention on Human Rights.

It is difficult to assess the merits of these arguments without seeing the full opinions. In general, however, the notion that statutory involvement in the regulation of the press is incompatible with the European Convention is a bizarre one. Many convention member states (with better records on press freedom than the UK) have some form of statutory underpinning or regulation. But what is most surprising is that Europhobic papers, usually implacably opposed to human rights and demanding the renunciation of the convention, are relying on these arguments at all.

When the Leveson proposals were debated in the House of Lords on 25 March 2013, Lord Black of Brentwood argued that the proposals on exemplary damages were "almost certainly contrary to European law" and so would "collapse or be struck down". Lord Black is executive director of the Telegraph Media Group. Telegraph newspapers have a very low opinion of the European Convention on Human Rights.

The Daily Mail was another of the newspapers which commissioned the "human rights opinions". It does not approve of the Convention. For example, it said it was "great day for British justice" when Theresa May said she wanted to withdraw Britain from the convention. Another commissioning group was News International. The hatred of its newspapers for the convention is too well known to need illustration.

The reasons for the antipathy of these newspapers towards human rights are no doubt complex. Some associate the Council of Europe with the hated EU. Some blame the Convention for the development of a law of privacy in England. Some blame the Convention for the inability of the government to deport suspected terrorists to countries where they may face torture. But the rationale which is usually given, sincerely or otherwise, is a democratic one: human rights arguments allow judges to overcome the will of Parliament.

For example, in an editorial last year, the Daily Telegraph told its readers that "The human rights act ... does not pass the test of popular legitimacy" and complained that Britain was "unable to maintain a ban on prisoner voting despite the will of Parliament". A few days ago, the Daily Mail published, and commented favourably on, an article by justice secretary, Christopher Grayling in which he complained that the Court of Human Rights "is demanding that countries including Britain override the will of their Parliaments, and make changes like giving votes to prisoners".

If you endorse this line of argument there can be no doubt where you must stand in the Leveson debate. The will of Parliament in relation to regulation of the press is crystal clear. The amendments to the Crime and Courts Bill bringing in exemplary damages and costs incentives for joining a self-regulator were passed by the House of Commons by a majority of 530 to 13 on 18 March.

Yet it appears that, in this case, the Mail, the Telegraph, the Sun and all the other principled opponents of the tyranny of human rights are prepared to make an exception. So far as Leveson is concerned, they want the European Convention on Human Rights to trump the will of the UK Parliament. These papers can’t have it both ways: if they have human rights which can override the will of Parliament then so do prisoners and foreign criminals.