, 75 per cent said there had been a fall in registrations, triggering a drop in pupil premium funding. And 30 per cent said the impact on their school had been "significant".
The school leaders estimated that an average 12 per cent of eligible pupils were not registered for FSM, meaning that schools were each missing out on thousands of pounds of government funding.
Hard to swallow
The research highlights the unintended consequences of the move to introduce universal free school meals for infants, a flagship policy of the Liberal Democrats. This week, deputy prime minster Nick Clegg announced that a Lib Dem government would roll out free meals to all primary pupils in England, with the pound;610-million-a-year plan scheduled to be introduced from 2017-18.
"Liberal Democrats want every child to have the best possible start in life. That's why I want every child to have a hot, healthy school lunch," Mr Clegg said.
The policy has proved less popular with some figures in the Conservative camp. Dominic Cummings, adviser to Michael Gove when he was education secretary, last year dismissed the policy as an expensive "gimmick".
The three main political parties' spokespeople for education - the Conservatives' Nicky Morgan, Labour's Tristram Hunt and the Lib Dems' David Laws - are all due to address the NAHT's annual conference in Liverpool this weekend. A motion at the conference will call for a national data-sharing system to be set up so that schools are automatically informed of pupils' entitlement to FSM, rather than relying on parents to tell them.
"The pupil premium and the universal meals are two really good policies that help children, but one is having a negative impact on the other," said Nicky Gillhespy, school business manager at Cheam Fields Primary School in Surrey, and a member of the NAHT's national executive.
"Because of the introduction of universal infant free school meals we've seen a big decline in parents registering for FSM, so the numbers of children entitled to the pupil premium has gone down," she added.
Alan Doyle, school business manager at Mount Primary School in Wallasey, Merseyside, said there had been a "marked drop-off" in FSM registrations at his school this year, resulting in a 19 per cent fall in pupil premium funding from about pound;105,000 last year to pound;87,000.
"The amount [of money] going out when pupils leave Year 6 isn't the same as the amount coming in [when pupils start in Reception]. So in a couple of years' time.the amount of pupil premium funding is going to be less," he said.
`A huge problem'
Data-sharing systems have been set up in a handful of local authority areas, including Bolton in Greater Manchester. The council's benefits staff notify schools as to which pupils are eligible, based on information from benefits applications.
Jack Hatch, executive headteacher of St Bede Academy, a primary in Bolton, said: "There's a huge problem in a lot of areas, where there's been a cliff-edge drop-off in free school meal registrations."
But the data-sharing system had resulted in the school receiving funding for "pretty much 100 per cent" of eligible pupils, he added. "It's all done behind the scenes. We've moved forward from the old days of everybody knowing that such-a-body is on free school meals."
NAHT general secretary Russell Hobby told TES it was "absolutely crazy" that schools were expected to "run around trying to persuade parents to register, when someone in the government already knows exactly who those families are and could share that with schools".
Meanwhile, a separate NAHT survey published today reveals that schools are spending pound;43.5 million per year on basic support such as food, clothes and showering facilities for children living in poverty.
"The education system is starting to operate a miniature welfare state that is being delivered ad hoc to fill the gaps that are emerging," Mr Hobby said.
`It isn't fair that children are missing out'
Nicky Gillhespy, school business manager at Cheam Fields Primary School in Surrey, says a typical year group at her school contains about 12 pupils who are eligible for free school meals.
"In the current Reception, two are registered," she adds. "We've never had a number that low before.
"If they're getting their free meals, there's no incentive for parents to register. And there's still a stigma in admitting they're entitled to these things.
"You don't want to be going up to parents in playgrounds and [asking them to register] in front of other people. It isn't fair that the children are missing out on funds they are entitled to."