The Department for Work and Pensions has been urged to ditch its "centrally controlled approach" and devolve funding and responsibility for its new welfare-to-work scheme to councils.
The Work and Health Programme is set to replace the DWP's Work Programme and Work Choice schemes when contracts for those programmes expire next year.
A report published by MPs last year found that the current Work Programme - which aims to provide targeted back-to-work support for welfare claimants with long-term health conditions and disabilities - was producing results "at least as good as before for a greatly reduced cost per participant".
Work Programme’s payment system was too complex, say MPs
DWP's Jobcentres could do much more to ensure people stay in work
But the Work and Pensions Committee said the programme was struggling to meet the needs of people with "more complex or multiple barriers to employment who need more intensive help", and pointed out that more than two-thirds of the programme's participants did not end up in sustained employment.
The new Work and Health Programme will have less funding than its predecessor, although the DWP is in the early stages of pilots with ten local areas that have Devolution Deals – including East Anglia, Greater Manchester, the North East Combined Authority, London and Liverpool – allowing them to co-commission support services.
The Local Government Association, which represents council chiefs, has now called on the DWP to grant councils much wider freedom to locally manage the WHP, and urged ministers to use the autumn statement to ensure the new scheme is "adequately resourced."
“Helping more ESA and long-term JSA claimants move into employment is crucial to boosting local growth and reducing the welfare bill," said Nick Forbes, senior vice chair of the LGA.
He added: "Councils know best how to do this. We know our local economies, we know our local employers and we know our residents and we can bring local services together in a way central government will never be able to.”
The LGA has put together its own plan for an "integrated" system of employment support to succeed the Work Programme, which would see funding and responsibility for the progamme fully devolved to groups of councils in England and Wales, going much further than the limited pilots so far in operation.
Cllr Mark Hawthorne, chairman of the LGA's People and Places Board, said: "Together with the government, we consulted councils on how the WHP should work. The clear message was that to be successful it will need to integrate local services, jobcentres must be required to work with councils and local partners so the right people are supported, and the right locally based contractors are utilised.
"Councils are committed to ensure no-one is left behind, but they simply cannot afford to pick up the local costs of long-term unemployment. The time has come for local government to be given the opportunity to improve performance by commissioning employment support from 2017."