After all the excitements of the Murdoch week it would be easy to imagine that the Leveson inquiry’s job of tackling press abuse in this country is done, or at least that the worst is over and the objective is in sight. Not so.

We might never have imagined that News International would be humbled in the public eye so much as it has been by this week’s interrogations and revelations, and it is hardly possible that the Murdoch family will ever again hold the power it once held, but let us remember the challenges that still confront the Leveson process and the cause of press reform.

One challenge is simple. No one in the press industry seriously believes that the practice of hacking mobile phones was restricted to a single newspaper or even a single company, and yet the inquiry has so far been unable to break down the wall of corporate denial.

Those denials are fundamentally improbable, partly because in the key period key players were moving between papers, and partly because those papers were so competitive. Do we really imagine that the News of the World kept its activities secret, or that its rivals were too scrupulous to copy it?

There is evidence, for sure – plenty of allegations – but there are no smoking guns, and on what is known to date it will surely be difficult for Lord Justice Leveson to state categorically that hacking was widespread.

Why does this matter? Because when it comes to his report, and to his inevitable demands for serious reform of the industry and its regulation, Associated Newspapers and Trinity Mirror will resist, will claim nothing illegal has been proved against them and will set about frustrating his objectives.

It is for this same reason that it is so vital that the evidence of widespread wrongdoing and illegality contained in the Motorman files is dragged out into the open.

Although the Murdochs may have been humbled, Associated and Trinity Mirror still have power. Not only can they blare messages from their front pages, but they also have influence behind the scenes. By the time Leveson reports in the autumn the dust of this week will have settled, and tabloid editors and proprietors will quietly be calling in favours and twisting arms again. They have allies in the Telegraph group; the Times and Sunday Times still have plenty of credibility, and there are big-gun columnists to make their case, not to mention leading politicians such as Boris Johnson and Michael Gove.

Of course there are other offences on the charge sheet besides hacking. The Mail, the Mirror, the Express and the rest stand convicted of multiple abuses in relation to Christopher Jefferies, the McCanns, Robert Murat, and an army of other people treated cynically and brutally. They stand convicted of years of deception about press regulation – telling the public that they were accountable when they all knew they had rigged the Press Complaints Commission in their favour.

But this is a temporary humbling, not unlike the temporary humblings seen before, for example 20 years ago at the time of the Calcutt Committee. Then, they wriggled and escaped. Is it possible that they are hoping for the same kind of escape again? It is not just possible; it is certain.

Look at the recent report of the Joint Parliamentary Committee on Privacy and Injunctions, which contained recommendations on press regulations, and look carefully at the voting records attached. It is impossible to find any logic in what went on, except a kind of desperate, try-anything rearguard action to avoid the clear and obvious conclusion.

Look, too, at Lord Hunt’s project for a son-of-PCC, whose raison d’etre is nothing more or less than the preservation of control of press regulation by the industry itself. Concessions are made to the need for something better than the old complaints handling service, but the essential characteristic of Hunt’s proposed regulator is that it is not independent of those it would regulate.

No wonder Lord Hunt says the industry is behind him. His proposal is being nurtured and groomed as an alternative to whatever Lord Justice Leveson proposes, so that ministers will always have a soft option to hand. Remember the uncertainty of the political future: at the best of times (whatever may be happening at the inquiry) politicians prefer press support to press criticism. These are not the best of times, and in the autumn an election will be that much nearer.

At the Mail, the Mirror, the Express and the Sun, and apparently also at the Telegraph papers and the Times and Sunday Times, there is no real sign that they have got the message from all that has happened at the inquiry. Look at their leader columns, which reek of denial. They are sullen and bitter, waiting impatiently for the moment to assert once again the power they have long regarded as their right.

There can be no doubt now that Lord Justice Leveson will recommend significant change in the autumn. Wounded as it may now appear, the national press remains fit and strong enough to put up a formidable and ruthless battle to keep the powers it is used to. If we want to see media reform, we cannot afford to rest now.

Brian Cathcart teaches journalism at Kingston University London and is a founder of Hacked Off. He tweets at @BrianCathcart

This post originally appeared on the Hacked Off blog and is reproduced with permission and thanks.