The Office for Civil Society is to ask private and charitable investors to purchase social impact bonds worth up to £40m that will fund new schemes to support "problem families".
"We must not be afraid to do things differently to end the pointless cycle of crime and deprivation which wrecks communities and drains state services," said Hurd. "Social impact bonds could open serious resources to tackle social problems in new and innovative ways."
Each council will devise a contract that specifies targets for families, which might include an increase in school attendance, a fall in criminal behaviour or a reduction in drug or alcohol abuse.
Charities and social enterprises will then bid for the contracts and find private and social investors to give financial backing.
If the charities meet targets specified in the contract their investors will receive a financial return. If they don’t, they may not get all their money back at the end of the investment period. Each council will work out its own system.
An OCS spokesman said Big Society Capital, formerly known as the Big Society Bank, might be able to offer some investment in the scheme.
The spokesman said it was not yet clear whether private sector firms would also be able to bid to run the projects, but that this would be decided by each local authority over the next few months.
He said the department estimated that the four projects would require a total of about £40m in working capital over a four-year period.
The OCS is not funding the projects, but has made up to £300,000 available to offer technical support to the councils in order to design the new tender documents.
Of the four councils, Hammersmith and Fulham, Westminster and Leicestershire are Conservative-controlled and Birmingham is run by a coalition between the Conservatives and the Liberal Democrats.
The OCS spokesman said the areas had been chosen because they had a significant number of "problem families" and because those local authorities were keen on innovative approaches to finance.
"The model is open to all councils to try, and all of the learnings from the pilots will be shared with all local authorities using an open-source model," he said.
Roberta Blackman-Woods, the shadow civil society minister, said: "Social impact bonds are an important innovation and this new trial builds on what Labour started in office.
"However, such initiatives should not be seen as a replacement for good public services."
The pilot projects are due to start in spring 2012, and tender processes to deliver the programmes are expected to open at the beginning of that year.