THE British press, for good or ill, has been free from state regulation for over 300 years. Many people, not least celebrities who have been hounded by paparazzi and phone hackers, believe predatory tabloids should be regulated, like the broadcasters.

Many on the left would also like to see Rupert Murdoch's media empire brought to heel. Labour MPs supported David Cameron's proposals, following the 2012 Leveson Report, for a Royal Charter to regulate the press. This state-appointed body would oversee a new system of low-cost arbitration in libel cases to give ordinary punters a chance against the Sun and the Daily Mail.

It sounded rather sensible. But the UK papers insisted state regulation is incompatible with a free press, and four years after the Leveson Report we can see why. The Government's Press Recognition Panel has nominated Formula One boss, Max Mosley’s organisation Impress as the official regulator. Worse, it has tried to force the press into accepting its remit by the most extraordinary piece of legislation ever proposed in a nominally free country.

Under Section 40 of the Crime and Courts Act, if newspapers don't sign up to the Mosley-financed regulator, they could be forced to pay the costs of both sides in libel and privacy actions, even when they win. So if the Sunday Herald exposes an MP as a crook, an athlete as a drug-taker, or a priest as a paedophile, he or she can take the publishers to court and, even if the story is true, the newspaper could have to pay their costs as well as their own.

Investigative journalism is already on the rocks; this could kill it stone dead. Even news pages could become anodyne and ingratiating as editors steered clear of stories that are true, but might provoke some important person to sue. Commentators would have to be intensely cautious about criticising anyone in public life – businessmen, politicians, university vice chancellors, other columnists – in case they took offence. Freedom of expression campaign Index On Censorship has condemned Section 40 as “jeopardising press freedom” and called the Government to scrap it.

Newspapers without deep pockets could be driven out of business, which is why many in the so-called “regional” press fear for its very existence. Libel lawyers could make a fortune urging everyone with a grievance, however flimsy, to go to court with no risk. It's not just no-win-no-fee, but no-win-they-pay.

The press reform group, Hacked Off, say draconian measures are necessary to force the press to accept low-cost arbitration. “The fact that dominant publishers don't like section 40,” it says, “simply shows that it is a meaningful incentive.” But the vast majority of newspapers and magazines, from Private Eye to the Guardian and the FT, won't accept Impress. They don't believe Max Mosley – who finances it – is a fit person to be involved in regulating the press. He won a sensational privacy action against the News of the World which had accused him of engaging in what was described as a "Nazi orgy". (A High Court judge found "no evidence" to justify that description.)

The UK Government consultation on Section 40 closes on Tuesday. The Scottish Government has confirmed that Section 40 will not apply under Scots law, which could throw another spanner in the works. Before the 2014 independence referendum, the Scottish Government appeared to accept that Scotland would remain under the UK’s regulatory regime under the proposed Royal Charter, but not this measure. Perhaps the entire London press would relocate to Scotland.

But is regulation really necessary? The press is already tightly regulated by law. Most of the offences examined by Leveson were already illegal: phone hacking, harassing children, stalking actresses and bribing police officers to get stories. Invasion of privacy and hate speak are against the law, and Britain's defamation laws are the toughest in the world.

There has been a string of corruption cases and civil actions in the wake of Leveson. Some journalists were jailed for hacking and bribing, some weren't. But following Operations Elvedon, Weeting and Tuleta, it's clear that failure to implement existing laws, not lack of regulation, was the problem. In particular, an unhealthy relationship had developed between the police and the press over many years which allowed corruption to flourish.

Of course, many celebrities still feel sore that their petty misdemeanours and personal foibles are paraded on the front pages of mass circulation tabloids – but that is a function of the celebrity culture from which they have benefited so magnificently. It is the public relations companies who manufacture and promote celebrities that have largely created this world.

The one area where Leveson was right to call time on the press was in their treatment of non-celebrities. It is difficult for ordinary folk to get legal redress when damaging untruths are reported about them. A teacher wrongly accused of being a sex criminal faces the financial hurdle of bringing a legal action against a big corporation like News International. Our legal system generally gives justice to those with deep pockets. However, press regulation is the wrong way to address this.

The press have set up their own body, the Independent Press Standards Organisation, IPSO, to police an editorial code. This is better than its toothless predecessor, the Press Complaints Commission, and has had some success in forcing papers to make apologies, print retractions and give other forms of redress. Admittedly, it is far from perfect, and even by its own standards has failed to restore public confidence. However, it is very difficult to find a form of state regulation which would be any better.

IPSO has agreed to introduce a low-cost arbitration scheme to handle claims against newspapers, which is currently undergoing a year-long pilot. Cynics believe it will come to nothing. If it does fail, perhaps some further incentive might be needed. Parliament is certainly right to put pressure on the press to improve its standards.

But by introducing a heavy-handed and frankly unjust legislation, Parliament has actually placed the moral initiative back with the very press barons they sought to discipline. Section 40 would be impossible in the US where freedom of speech is enshrined in the constitution. It is an abomination in a democratic country and must be scrapped. You can't seek to make the press more responsible by punishing it for telling the truth.

Moreover, Leveson has been overtaken by events. Since his report on press regulation was published in 2012, the media has changed out of all recognition. Newspapers have lost out to social media websites like Facebook and Twitter which don't have any regulation whatever, and seem to be immune even to the laws of defamation and hate speak. If someone posts a defamatory comment on a newspaper website, the newspaper gets sued; if the same comment is posted on Twitter, the person who made the comment may be sued, but Twitter is scot-free. Newspapers have to go to the expense of moderating all the posts on their websites, a burden their internet equivalents do not have to bear.

It is extraordinary that the law has failed to understand that websites like Facebook are exactly the same as newspaper websites, except that they don’t pay for their own journalism; they either plagiarise the established press, or recycle material provided by followers and websites that recycle conspiracy theories. The Government and Parliament are trying to regulate the press when most of the public now get their information from completely unregulated internet sources that don’t observe the most basic standards of accuracy or fairness; that publish fake news and all manner of misogynistic and racist abuse with impunity.

These sites are hugely influential, as we saw in the US presidential elections, yet the UK Government is trying to impose even greater cost pressures on the only people who still have some respect for journalism: the press.

It's time politicians woke up to the real problem facing civil society and tried to introduce some basic legal standards into the wild west that is new media. If measures like Section 40 remain, there may soon be no press left to regulate.