Control over programmes to get the unemployed into work should be handed to cities, according to the mayor of London, Sadiq Khan, and the frontrunner in the race to be mayor of Greater Manchester, as a new report suggests huge savings to the taxpayer could be made by the move.

Leading thinktank IPPR North claims that devolving the government’s current work programme could boost employment by freeing up funding for established and innovative ways of getting people into jobs.

As much as £9,000 could be saved for each benefit claimant if the work programme were devolved and mayors given freedom to use innovate methods, it is claimed.

The IPPR’s report claims the current programme, run centrally by the Department for Work and Pensions, is not sufficiently sensitive to local conditions and lacks the funding it needs to help the most vulnerable into work.

Khan called for the new prime minister, Theresa May, to act on the report to allow London to best deal with the consequences of Brexit. “The best way to protect London from the economic fallout of leaving the EU is for the government to grant more autonomy to the capital, so we have more control over how taxes raised in our city are spent and how public services are run,” he said.

“As part of this, it is clear that London should have direct control of the work programme so we can better help Londoners to find employment.

“I have spoken to London’s political and business leaders regularly over the past month and it is clear that further autonomy is key to ensuring London’s continued economic success.”

Andy Burnham, the shadow home secretary, who looks set to be Labour’s candidate in the 2017 election for the first mayor of Greater Manchester, said that he would ensure that the city’s welfare policies were effective and free from the “cruel, tick-box, sanctions-based” regime run from Whitehall.

He said: “Rumours that Theresa May has gone on cold on English devolution are deeply concerning. It is helpful to have such authoritative backing from the IPPR for a call I made on the prime minister this week.

“The right response to the EU referendum result is not to abandon the devolution journey but to deepen it.”“The exclusion of DWP from the devolution settlement in Greater Manchester leaves a missing piece in the jigsaw. If I am mayor of Greater Manchester, I will make an immediate case for the devolution of the DWP budget. I am certain that by linking it with our voluntary and community organisations, we can do more to help people than the cruel, tick-box, sanctions-based DWP regime.

“The referendum result reveals a deep disenchantment with the way Westminster works. It has given us a very unequal country and the time has come to balance it.”

The IPPR North’s report claims that mayors or local authorities would be better placed to invest-to-save.

The tax-benefit saving for a moving a single man living in council tax band C private rented sector housing in Sheffield from long-term job seekers allowance into a minimum wage job for 30 hours a week is £8,600 per year, the report says.

The annual tax-benefit saving for moving a single woman on employment and support allowance, living in council tax band C private rented sector housing in Southwark, who moves into a job paid at £8.25 per hour, is £9,000 for a 20-hour week.

Josh Stott, head of cities at Joseph Rowntree Foundation, which commissioned the report, said: “The UK is benefittng from record levels of employment which is welcome news. But many people, particularly in the north, are locked out of the country’s prosperity because they don’t have skills or the right level of support to find a suitable job.

“These proposals recognise the opportunities that greater devolution can provide – more joined-up, efficient and effective support for people out of work and incentives for town halls to foster more inclusive growth.