Britain has undergone a "slow-motion moral collapse", David Cameron will say today, as the cross-party unity that had marked politicians' responses to the riots begins to crumble.

The prime minister will go head to head with the leader of the opposition as the two make speeches setting out their competing analyses of the riots and looting. The pair make similarly emphatic condemnations of the rioters, but in a speech at his old school in Camden, Ed Miliband, the Labour leader, will denounce Cameron's ideas to deal with rioters, put forward over the weekend, as "gimmicks".

Miliband will also link the behaviour of the looters and bankers, phone hacking and MPs' expenses scandals, saying: "It's not the first time we've seen this kind of me-first, take-what-you-can attitude. The bankers who took millions while destroying people's savings: greedy, selfish, immoral. The MPs who fiddled their expenses: greedy, selfish, immoral. The people who hacked phones to get stories and make money for themselves: greedy, selfish and immoral. Let's talk about what this does to our culture."

Today, Cameron will push his long-held opinion that parts of Britain are broken, despite opinion polls that show the public believes he has not handled events well. He will say today that government ministers from both parties will audit their portfolios for policies aimed at mending the "broken society".

In the speech, to be delivered outside London, Cameron will say: "Over the next few weeks, I and ministers from across the coalition government will review every aspect of our work to mend our broken society, on schools, welfare, families, parenting, addiction, communities; on the cultural, legal, bureaucratic problems in our society too; from the twisting and misrepresenting of human rights that has undermined personal responsibility, to the obsession with health and safety that has eroded people's willingness to act according to common sense – and consider whether our plans and programmes are big enough and bold enough to deliver the change that I feel this country now wants to see."

His words suggest again that the government is angling to renegotiate European law, which can overrule domestic legislation, and which they believe has prevented them from devising policies as they would like.

"Irresponsibility. Selfishness. Behaving as if your choices have no consequences. Children without fathers. Schools without discipline. Reward without effort. Crime without punishment. Rights without responsibilities. Communities without control. Some of the worst aspects of human nature tolerated, indulged - sometimes even incentivised - by a state and its agencies that in parts have become literally de-moralised."

He will say he believes that the public are "crying out" for the government to act in this way, and that "I will not be found wanting". His passion to mend broken society is, he will say, "stronger today than ever".

Miliband, thought to be speaking at the same time, will be at Haverstock comprehensive, in Chalk Farm, north London. The route Miliband would walk to school was hit by rioters last week.

Miliband will reflect on ideas floated over the weekend by Iain Duncan Smith, the secretary of state for work and pensions, who has been appointed to lead a gangs task force. Duncan Smith said the government would begin "harassing" gang leaders, suggesting dusk-till-dawn curfews, daily visits and a trawl of their lives and finances to pick up minor infringements.

Gang members possibly should, Duncan Smith suggested, receive a knock on the door once a day from the police and arms of government such as the TV licensing offices, tax authorities and DVLA.

Children out late at night would be offered places at newly created young offenders' academies to "take the anger out of their lives".

Miliband is pushing for a national inquiry. He will say: "A new policy a day, knee-jerk gimmicks unveiled without being properly thought through, are unlikely to solve the problem."

The Labour leader will also taunt the prime minister, saying that when Cameron was developing his analysis of "broken Britain" in opposition he acknowledged that deprivation mattered as much as culture in explaining antisocial behaviour.

Miliband will say: "I don't understand why he has changed his mind. The world hasn't changed. Maybe it isn't his view of the world that has changed, but his view of what would make him popular that has changed. I am clear: both culture and deprivation matter. To explain is not to excuse. But to refuse to explain is to condemn to repeat."

Duncan Smith, meanwhile, publicly criticised Boris Johnson, the mayor of London, for failing to grasp that London's main crime problem is gang culture, not knife crime. Johnson, however, told Sky News yesterday that he wanted an increase in police numbers, saying he was "obsessed" with his cause. He told Sky: "The case I make to the Government, and I'm going to continue to make, is that numbers matter, and I think that the numbers we have got on the streets in London now they're up on when I came in [as mayor]."

Though official line of the Lib Dems was steadfast in support of the new agenda, with a spokesman saying Lib Dem justice minister Lord McNally was likely to be appointed to work on Iain Duncan Smith's gangs taskforce, and saying they did not rule out some of Duncan Smith's proposals floated over the weekend.