The free schools policy has been criticised for being socially divisive, handing cash to largely middle-class groups to set up new schools that can “poach” pupils from existing ones.
The majority will be in the South, while crumbling schools – including scores across Merseyside – lost funding for rebuilding with the dismantling of the Building Schools for the Future (BSF) programme.
Mr Twigg said he was determined to ensure the shrinking pot of money for capital projects was spent fairly, including on schools with “leaking roofs and asbestos problems”.
But he said: “On free schools, I am saying that we need to apply a set of tests, that we are not going to take an absolute policy of opposing them.
“The tests should be: will the school raise standards for pupils and parents, will it contribute to a narrowing of the achievement gap between rich and poor and what is the wider impact of that school?”