For 20 torrid years, from the mid-1960s to the mid-1980s, "Who governs?" – parliament or trade unions – was the central issue in domestic politics. In 1969 Harold Wilson's Labour government tried, in Barbara Castle's In Place of Strife white paper, to bring the unions within the law. The unions, and a significant part of the Labour party, fought off the attempt.

Ted Heath's Tory government tried again in the 1970s, and was driven from office. Jim Callaghan's Labour government ceded the unions a share of power, but he fell because of the unions too. Margaret Thatcher succeeded where Heath had failed, at traumatic cost to the unions – partly self-inflicted – that persists to this day. Yet for the past quarter-century, the "Who governs?" question has had its answer – the right one: parliament governs, through the law.

The question still matters in Britain today. It matters in a different context, yet the terms are strikingly familiar. Do the elected government and parliament govern? Or are we governed instead by those who also believe, as a matter of fundamental principle and as the unions also once believed, that the law should not apply to them?

Today two groups are the equivalents of the unions of yesteryear. The first are the boardroom tax avoiders, whose corporate and individual taxes, if paid as intended, would transform the public finances from deficit to surplus in an instant. The second group is the British press, with its collective interest in weak government. All these groups have in their time been referred to as barons: trade union barons, boardroom barons and press barons. Barons ultimately believe in their own unrestricted power – though they call it freedom.

Unless something improbably statesmanlike happens in the next few weeks, it is increasingly clear that the press has now defeated parliament's two-year attempt to bring it within the rule of law. The Leveson report, published last November amid so much hope for much needed change following the phone-hacking scandal and much else, has failed. Its 2,000 pages are history.

Today the Leveson report is to press reform what In Place of Strife was to union reform. (We haven't even got to first base on tax avoidance reform.) Harold Wilson flirted with union reform after the seamen's strike in 1966 and then got scared off in 1969. David Cameron has done the same thing, flirting with press reform after the phone hacking scandals in 2011 before getting scared off in 2013. In both cases vested interest triumphed. In 1969 the Daily Mirror ran a front-page editorial headlined: "There exists in Britain a power outside parliament as great as that which exists within." Today there is again a power outside parliament whose power exceeds parliament's – the press.

In the six months since Leveson was published, many have presented the report as an attack on the freedom of the press. Some may believe, genuinely, that this is what is at stake. While accepting the seriousness of the issues, I disagree entirely. I disagree as regards most of the particular effects of Leveson – though some of these are negotiable. But I disagree more fundamentally with the larger assumption, which rests on a false and foolish view both of the nature of the state and the law, and the nature of freedom – a view that no state should make any law regarding the press, even if it is to uphold its freedom.

In the course of the post-Leveson debate, a great principle – the free press – has been shamelessly hijacked by vested interests. Freedom has been elided with press self-interest. Press opposition to reform has been brash, heavy-handed and single-minded. Even the extraordinary all-party agreement in March to put significant parts of Leveson under the umbrella of a royal charter caused only momentary hesitation. In the end, not even the fact that no single MP voted against the agreement counted for anything. The press ignored parliament's verdict. It simply resumed its battle to stop it from coming into effect. And now, with its own counter-charter, it has seemingly succeeded.

All this brings to mind an exchange in Tom Stoppard's Night and Day, quoted by Leveson, in which one character says: "No matter how imperfect things are, if you've got a free press everything is correctable, and without it everything is concealable" – to which another character replies: "I'm with you on the free press. It's the newspapers I can't stand." But the outcome also has darker echoes of the attitude of America's National Rifle Association, which will never be deflected from defending what it regards as an absolute principle by any evidence or any form of compromise or reform, however modest, needful and widely supported.

It is possible that parliament's charter will in fact be created later this month, and that the press's counter-charter will fall by the wayside. But the political dynamic of reform will continue to falter. Parliament's charter will be still-born. It will create a recognition body that much of the press will spurn. The path leads only downhill. The Tory party's heart, torn about the charter option even today, will harden against it by 2014, with a general election imminent. It would be reckless for Labour or the Liberal Democrats to embark on anything tougher on the eve of the campaign. It stretches belief to imagine that even prime minister Miliband would want to pick such a fight with the press in the difficult circumstances of a Labour government. This is a failure for a generation, as Wilson's was in 1969.

So now our generation has its answer. The press has more power than parliament (as the tax avoiders do). Britain's unbound and politicised press has gambled on politicians' unpopularity and Cameron's weakness – Ukip local election success on Thursday will help the process – and is winning. It thinks that, come the election, Cameron's need for fully armed press allies will trump his need to keep his word on press reform. It is surely right.

Can anything be done? Perhaps Sir Brian Leveson himself could re-enter a debate that has spiralled away from what he proposed. That would help. But Leveson is lying low and hoping to become lord chief justice, they say. But if I chaired the Commons culture, media and sport select committee, I would summon Sir Brian, Robert Jay, the McCanns, the Dowlers and Chris Jefferies, in the hope that they could create pressure to stiffen Cameron's resolve.

But this is a mix of "Who governs?" and "Who's chicken?" The answers are alarming. The press governs. And Cameron is chicken. Leveson was the moment. And Cameron flunked it.