The design and technology curriculum will be introduced from September for key stage 1-3 children, aged from five to 14. It will feature practical cooking and food but not gardening.
Former Garden Organic chief executive Bremner said: "It's clear children aged five to 14 need to understand where food comes from, why food is important and be able to practically cook and grow food. The word 'horticulture' was taken out of the curriculum to show it's about food.
"Gardening is not in the final draft but the wording gives schools and delivery organisations every opportunity to continue the fabulous work they're doing with school gardens."
He said a "whole school approach" to weave food education into learning is important, including a school garden. The School Food Plan has 17 "actions" such as more breakfast clubs and school meal provision.
At a School Food Plan in-practice conference at Charlton Manor Primary School in London, chef Raymond Blanc said gardening should also be part of the curriculum as well as food.
Also at the conference, Blue Peter gardener Chris Collins, who is set to present for Thompson & Morgan on Ideal World TV, gave tips on engaging children in gardening. He said schools should tap into private equity riches through corporate social responsibility schemes.
Chef Levi Roots said following his Caribbean background of growing produce could help children learn about foods' origins.
Blanc advocated producing herb omelettes while Roots said growing and making fruit smoothies is among the top tips for children.