The chef and food rights campaigner Jamie Oliver has said there is a need “now more than ever” to expand the number of children eligible for free school meals.

Speaking on BBC Radio 4’s Today programme, Oliver said the benefits and income threshold that parents must meet for their children to be eligible for free school meals should be lowered.

Children of parents who are on universal credit and have an annual income of no more than £7,400, or are on another benefit such as jobseeker’s allowance, are eligible for free school meals.

Oliver said: “If you earn over £7,400, you won’t get that free school lunch. But I think we’d all agree that there’s a massive gap between the means test for free school lunches as it stands and universal credit.

“I think what the government are saying is universal credit tethers off and can go up to sort of £30,000 to £40,000, but really we’re talking about the bulk of them being around £14,000 per household.”

Asked if he wanted the threshold to be met, he replied: “Well, now more than ever … if they were to open the threshold of who would be allowed to have a free school lunch, that would also inject funds into the system that would also really help to guarantee a much better service across 26,000 schools in the country.”

Oliver, 47, told Today the former prime minister Boris Johnson had to “nearly die and have a child” before he saw the chef’s point of view over school lunches.

Asked about getting Johnson “on side” after “having warred with him” over free school meals, Oliver said: “He had to nearly die though and have a child to put him in the frame of mind to do the right thing.”

Oliver was asked by the programme if he was part of the “anti-growth coalition”, a term coined by Liz Truss, the prime minister, for a large and wide-ranging group of people who believe her economic plans for the UK will be disastrous.

He replied: “Completely not. I’ve spent a lifetime not only employing over 20,000 people but travelling around the world saying how brilliant Britain is.

“That’s what we need to do as a country. We have an incredible country but just doing quick trade deals to the lowest common denominator and threatening British farming and British producers is completely bonkers.”

He added: “The reality is, if you speak to the best minds in economics, in the country, in the world, they will tell you that if you output healthier kids, you’re going to have a more productive, more profitable country, better GDP. To do that, you have to think in 10 to 20 years, not three-year cycles.”