Tom Middlehurst, from the Association of School and College Leaders, said improving the quality of school food was “something we wholeheartedly support”.
He said the changes “must be implemented in a practical way”, including with additional funding to pay for any increased costs.
Munira Wilson, the Liberal Democrats’ education spokesperson, said the government “needs to ensure that free school meals funding matches the rising costs, ensuring every child receives a healthy and filling meal essential for their education”.
“From talking to parents, head teachers and school governors in my constituency, I know that many are worried about the rising cost of food, and in many cases the current funding just isn’t enough, forcing schools to provide smaller portion sizes and poorer quality food,” she said.
“The education secretary must urgently address this problem.”
A spokesperson for Reform UK said the plans were “yet another example of the government trying to micromanage people’s lives”.
“Banning foods from school menus won’t solve childhood obesity,” they said.
“It just removes choice and adds pressure on already stretched schools. We should be focusing on education, personal responsibility, and ensuring families can afford healthy food, not headline-grabbing bans.”
A spokesperson for the Green Party said: “Removing unhealthy food from school menus is welcome and long overdue.
“We believe free healthy school meals should be offered to all primary and secondary pupils, not just infants.
“Real change also means tackling the root causes of the 14% of households facing food insecurity – the cost of living and low pay.
“Greens also want to see our food and farming system transformed so it prioritises affordable, healthy food with fair wages for growers.”
BBC News has also approached the Conservatives for comment.