A scheme to encourage organisations to establish chains of schools was extended to primaries this week.
The "accredited schools" kitemark covers groups that want to be academy sponsors or lead school federations or trusts.
Prime Minister Gordon Brown announced the first 13 organisations approved to lead secondary schools and said the initiative would be extended to primaries struggling to reach high standards.
Schools Secretary Ed Balls added: "Over 5,000 more primary schools are above the floor target compared to a decade ago, but there are some who still need extra support and help.
"We expect local authorities to look to primary-accredited school groups when looking at bringing about rapid and sustained improvement in their primary schools."
But Christine Blower, general secretary of the NUT, said: "There is absolutely no evidence that sponsors, tied in to the governance of schools, do anything other than restrict those schools' ability to have wide and flexible relationships with organisations in the outside world.
"Instead, sponsors are there to take over the running of schools and impose their particular views of how schools should be run."