F ree, critical press and media arevital for our country and an essential part of holding the powerful, including politicians, to account. The journalism that uncovered the Cambridge Analytica and Windrush scandals shows the press at its best. But that vital freedom of the press cannot be a licence for a small minority to trample on the lives of innocent people or to engage in, sanction or cover up criminal activity. This was a truth universally acknowledged, including by politicians and press, after the revelations over the hacking of Milly Dowler’s phone in 2011.

On Wednesday a cross-party group of MPs, including Ken Clarke and myself, will seek to win support for an amendment that will keep the promise of a “Leveson part two” inquiry into the press and social media, rather than abandoning that inquiry as the government wishes. We are doing so because, above all, we owe it to the victims of phone hacking and other wrongdoing to get at the truth about what happened and learn lessons.

In the wake of the revelations of 2011 David Cameron established the Leveson inquiry in two parts. Part one looked at the general set of issues around the culture and ethics of the press, and the relationships with politicians and it made recommendations for regulation. It was not able to look at specific allegations because of ongoing criminal investigations.

It was only after these concluded (which happened in 2016) that part two was to look at “who did what to whom” in the words of Brian Leveson and how executives, politicians and the police allowed it to happen. After Leveson part one, Cameron said: “One of the things that the victims have been most concerned about is part two of the investigation should go ahead … It is right that it should go ahead and that is fully our intention.”

Leveson himself is emphatic that it must go ahead. This is about honouring our previous promises to the victims, but also about the future. How can we act to protect the public if we don’t know the facts about what past abuses happened and why? How can politicians be trusted to ensure fair play for victims if we don’t deliver on our promise to see the process through?

There is also real urgency in investigating new issues thrown up by the dissemination of news and information on social media. That is why, as Leveson himself recommends, the whole issue of fake news and misuse of personal data by Facebook and social media platforms is an essential element of part two.

After Leveson part one, David Cameron said that, “One of the things that the victims have been most concerned about is part two of the investigation should go ahead … that is fully our intention.” Photograph: Rex Features

The word of the senior judge chairing the inquiry would normally be enough, but some in the press, and government, are desperate to stop the inquiry happening. Their arguments are wholly unconvincing.

They claim it would be “backward-looking”, but it’s obvious that we need to look carefully at the past so we can learn from it. The necessity of getting to the truth cannot be time-limited. The press would rightly not tolerate this approach in any other industry or institution where there had been such significant wrongdoing.

They say the police have already looked into the wrongdoing at newspapers, but narrow and unpublished police investigations are no substitute for the public airing of the broad range of evidence in front of an impartial judge.

We are told that any wrongdoers have cleaned up their act, but the recent Kerslake report on the Manchester Arena bombing expressed “shock and dismay” at reporters’ intrusive treatment of stricken families. And recent weeks have seen whistleblower allegations of years of bank account hacking by the Sunday Times.

Nor can we take comfort from the response to Leveson part one. The press declined to set up the kind of independent regulator that both Leveson and parliament wanted to see. Instead we have Ipso, a toothless organisation that, despite bold promises, has yet to impose a single fine or deliver a single equal prominence front-page correction in a national paper. There are also significant issues around the lack of rules or redress around much of the news on social media.

Opponents claim that completing part two would somehow undermine the local press, but that’s wrong too, because local publishers are explicitly excluded from the inquiry into what happened in the terms of reference we propose.

It was Cameron who in testimony to the inquiry said its true test was: “not ‘Do the politicians or the press feel happy with what we get?’ but ‘are we really protecting people who have been caught up and absolutely thrown to the wolves by this process?’” It is time to apply that test.

We should honour the promises made to the victims and vote for the completion of this inquiry. That is the only way we will get truth and justice – and media, old and new, that command public trust and confidence.

• Ed Miliband is the Labour MP for Doncaster North and was leader of the Labour party, 2010-2015