The PM prepares vegetables with the users of a community centre in Smethwick, West Midlands / Reuters

Critics say government funding will be enough to help only one in five troubled households

David Cameron faced charges yesterday of failing to put enough money behind an ambitious drive to "get to grips" with 120,000 of the country's most dysfunctional families.

The Prime Minister announced a £1.1bn programme to offer targeted help to households linked to high levels of truancy, crime, violence and anti-social behaviour.

He said such households should not be written off as "worthless or pre-programmed to fail" and that a network of "troubleshooters" would help them to tackle the root causes of their disruptive behaviour. This would benefit the whole of society, he added.

The Government is providing just under £450m over the next three years, with the rest of the cash coming from councils. Critics warned that the spending squeeze on town halls would undermine attempts by local authorities to find the cash for the scheme.

They also said that £450m would only be enough to work successfully with between 20,000 and 25,000 families. Matt Cavanagh, the associate director of the centre-left think tank the IPPR, said: "There is still a big question mark over whether the funding will be enough." In a speech in Birmingham, Mr Cameron spelt out the Government's definition of a troubled family and said it estimated that nearly 120,000 households fit that description in England.

Ministers believe that for a family to fall into the category, it must fulfil five out of seven criteria: no one is in work; the family's income is low; it has poor accommodation; no one has a qualification; the mother has mental-health problems; a parent has a long-term illness or disability; the family cannot afford all the food and clothing it needs.

Local authorities will be asked to identify the problem families in their area by February and draw up plans for visiting and helping them.

The project will be overseen by Louise Casey, the head of the new Troubled Families Team. Families that refuse to co-operate could lose benefits or be threatened with eviction, but Mr Cameron argues that the vast majority want help.

He said a targeted approach could "work wonders" with families. "This immense task will take new ways of thinking, committed local action, flexibility and perseverance," he said. "But I know too that it's a task we can't shirk. We must get out there, help them turn their lives around and heal the scars of the broken society."

But Helen Dent, the chief executive of the charity Family Action, called for extra resources for councils. She said: "We would like to see further investment in early intervention and the early years."

Labour said the cuts to town hall budgets, including money for Sure Start programmes, ran counter to the Government's good intentions.

The former Home Secretary David Blunkett said he was worried that "we're taking with one hand while giving with the other".

Problem family? The seven criteria

* No-one in the family is in work.

* The family is living in poor or overcrowded housing.

* No person has any qualifications.

* Mother has mental health problems.

* At least one parent has a long-standing illness or disability.

* The family has a low income.

* The family is unable to afford a number of food or clothing items.