Money saved by scrapping free school meals for half a million primary school children will be used for a scheme under which groups compete for cash to improve England's worst-performing schools.

Academy sponsors, councils and headteachers with an outstanding track record will be encouraged to bid for funds to turn around struggling schools in a contest that will reward those that offer the most ambitious plans for reform.

The cash will come from an endowment fund started with £110m of public money, saved by a coalition decision to scrap an extension of free school meals to all primary schoolchildren living below the poverty line. The government plans to outsource the project to a City fund manager, who will assess the bids in consultation with education experts. The education secretary, Michael Gove, said he expected the fund to pay out up to £10m a year.

He said: "We will invite bids from people who want to turn round under-performing schools and the bids will be assessed on the degree of ambition and rigour they show.

"Are they ambitious in showing a clear path of improvement for under-performing schools, and are they rigorous in showing the money will be used either to develop already tried and tested methods of raising attainment, or pioneer new ways of raising attainment?"

The money could be spent on monitoring the performance of individual teachers, extending the school day, or providing one-to-one support for some children.

The funding, which will come on top of the pupil premium, could also lead to higher pay for teachers who generate the best results. Gove said: "My view is that, while I can think of some of these things, the purpose of the fund is to generate a greater degree of innovation." He compares the fund with Barack Obama's Race to the Top initiative, under which US states compete for federal cash.

The announcement is timed to coincide with a visit to Britain by the US education secretary, Arne Duncan, who will meet Gove and tour Mossbourne academy in Hackney, east London, tomorrow.

Gove said: "America is a bigger country and there are differences between us, but I have been impressed by what Race to the Top has done, and impressed by many of the things that President Obama and Arne Duncan have been fighting for."

The last government had intended to extend free school meals, which are currently available only for families receiving unemployment benefit. Labour planned an extension to families below the poverty line, which is calculated at £19,500 a year for a couple with two children.

Gove said: "No one who's currently eligible for free school meals will lose out, but we believe that it is more important to use this money to support measures to raise attainment."

Under the plans, a number of struggling schools that are currently run by councils will become academies, and the government is determined to override councils that attempt to block this transfer of authority.

"Some of these schools are schools that local authorities themselves have identified. They want an academy solution," Gove said.

"I'm clear also that one of the reasons we passed the Academies Act is that if we do have a local authority that refuses to take action and you have a school that has been permanently failing, that the local authority cannot act as a block to that school becoming an academy if that is the right answer in those specific circumstances."

Rather than creating a new quango, the funding will be dispensed by an existing philanthropic foundation.

The Education Endowment Fund will run for a decade, dispensing money from its income as well as a portion of the capital each year. The government hopes it will also encourage donations from philanthropists. Establishing it for a decade will put it outside the "twists and turns" of Treasury negotiation, Gove said.

"[If] you're a philanthropist, you want to put something back into education, but you don't necessarily want to get involved in the academies programme, that's fine. This is a direct route for you to be able to know that your money will go to help turning around under-performing schools and there will be a rigorous monitoring of how that money will be used.

"You can feel confident that you're making a direct and measurable contribution to eliminating disadvantage."

Schools will be judged eligible based on their results and their degree of improvement. The scheme will be open to both primaries and secondaries and ministers expect the money will go to "hundreds, not thousands" of schools in England.