Free school meals for all pupils, whether rich or poor, improves behaviour, says an expert who studied the UK's only substantial test project.
A project in Hull tested free healthy meals for three years
Children in five areas of Scotland are set to take part in a pilot scheme where all primary pupils will be able to have free meals.
The idea was previously tested for three years in Hull - before being scrapped on grounds of cost.
But researchers said better diets had produced "calmer classrooms".
Professor Derek Colquhoun from the University of Hull carried out an evaluation of the free school meals project - and is set to publish a full report early next year.
Hungry to learn
Professor Colquhoun, who is also an adviser on the Scottish projects, says the Hull experiment was a clear success - and that it was a "tragedy" that it had not been extended.
This Eat Well, Do Well project, which ran from spring 2004 to summer 2007, provided free healthy breakfasts, lunches and after-school meals for all primary pupils in Hull, without any means testing.
The idea was to see whether providing healthy meals without charge would have an impact on pupils' health and readiness to learn.
And Professor Colquhoun's interim report concluded that there had been a "significant impact across the city" - with calmer classrooms and children who were more aware of healthy eating.
The findings were based on interviews with head teachers in the city - who reported improvements in behaviour.
He also noted that pupils were less likely to complain of being hungry in the afternoon - and that pupils in the city who had been eligible for free school meals were on average 3.8cm shorter than those who did not qualify for free school meals.
Take-up of the free school meals had risen to 65% - with most of the remainder bringing packed lunches.
And Professor Colquhoun's findings suggested that raising the number of people who had eaten hot, healthy meals during the day brought an overall improvement to the mood of the classroom.
This included better results in the afternoon in tasks that required concentration.
"Classrooms in the city are calmer now because more children are getting a balanced meal at breakfast and lunchtime," he said. "And the free school meals project could also lead to less incidences of bullying."
The free meal scheme, the first of its kind in the UK, was stopped in summer 2007, when the incoming Liberal Democrat administration decided not continue the project.
A council spokesperson said that the decision was taken on cost grounds that children from families which could afford to pay should not be given a free meal.