Ed Miliband has become the first political leader to call for an independent review of newspaper regulation and practices after the admission by News International that it hacked into the phones of celebrities and politicians then failed to carry out full inquiries into the wrongdoing.

Miliband told the Guardian: "I think there does need to be a review after the police inquiries have been completed and any criminal cases that flow from it.

"I think it is in the interests of protecting the reputation of the British press that these matters should not simply be left to rest, and lessons have to be learned."

He is aware that a front-rank politician, especially a party leader, is taking a political risk by challenging the media over its practices, including the powerful News International stable, but he argued: "The press itself will want to look at how self-regulation can be made to work better because it clearly did not work very well in relation to these issues here."

He went on: "What happened was very bad, and it is right to say that, but there are very good traditions in our press, and they have to be maintained, but we have to get rid of the bad ones, and we have to find a way of doing that."

He argued: "My strong instincts are that we do not want governmental regulation of these issues, but I don't think the Press Complaints Commission has covered itself in glory."

The PCC, chaired by the Tory peer Lady Buscombe, is responsible for newspaper regulation and has been widely criticised for failing to challenge News International over the scale of phone hacking.

Miliband said: "It is not about government imposing this on the press, but I think the review needs to have some independence, both from government and from those involved in the day-to-day running of newspapers. I think that would help the industry. There has to be a sense that the future is not going to be like the past. Wider lessons have to be learned." He stressed he had no grand plans about who should run the inquiry.

Labour is aware that Lord Fowler, the chairman of the Lords communications select committee and a former Conservative party chairman, has been calling for a judge-led inquiry into the newspaper industry.

Miliband added: "I would separate out the backward looking issue of who did what wrong, and any criminalitity, on the one hand and the forward looking issue of what lessons need to be learned."

He stressed: "The immediate priority is to have this police inquiry, for it to do its work and to get to the bottom of what really happened. We now know because News Interantional have said so the media did some things they regret. This inquiry has got to take its course and it is very important it does that".

He added: "My clear view is that self regulation continues to be the right thing. We do not want the government regulating the press."

He was also pleased the police were investigating suggestions that newspapers regularly paid police for stories. "The first police investigation clearly did not uncover the full facts, but in the second investigation they seem to be going about it the right way, and I am sure they too will want learn lessons from it."

In a wide-ranging interview while on the election trail, Miliband also disclosed he was engaging closely with the so-called "Blue Labour" project associated with Lord Glasman, the controversial political theoretician ennobled by Miliband.

Glasman has argued Labour has become disconnected from its traditional working class voters by developing a top-down model of government that became remote, bossy and managerial.

Miliband said: "People value local institutions in their lives that go beyond the bottom line from the local high street, the local post office, the NHS and the local Sure Start. Local people have got be able to have more say about their area, its character and whether they have a local Tesco. People have got to have more say about 24-hour drinking and nightclubs, and what is changing in their area. We need strong communities."

He said he disagreed with Glasman's claim in a forthcoming interview that Labour caused a massive rupture of trust by lying about immigration, but said the party had to talk more about the big issues underlying immigration's impact on working-class people, including the undercutting of wages.

"I don't agree we lied," he said. "We underestimated the impact of eastern European migration and flexible labour markets. The two came together and we got aspects of that badly wrong."

He also said the elections on 5 May represented "a chance to change the contours of British politics for the rest of the parliament" and he did not rule out the coalition imploding if the Lib Dems were hit hard.

Nick Clegg had made a fundamental mistake in aligning himself with the Conservatives and becoming a prisoner of David Cameron, Miliband argued.

He suggested trust in the Lib Dem leader had been destroyed. "There is a fundamental lesson about politics – if you go round making promises and then breaking them, it is disastrous for you personally and pretty bad for politics generally, and that is what has happened.

"When you say you are going to vote against rise in tuition fees and parade round students saying that and then do the opposite, it just makes people cynical and jaded."

He also promised to say more about the Labour government's mistakes. Faced by polls showing the party is blamed by most people for the deficit, he accepts "there is more work to win back economic credibility".

He added: "We have been very clear about mistakes on bank regulation and the fact that we did not build a broad enough industrial base.

"We should have acknowledged earlier that our four-year deficit reduction plan did involve spending cuts, but what I am not going to do is to buy into the Tory argument that the deficit is all the fault of Labour overspending.

"It is not true, it is just not true, I am not going to say because it is not the case."