Hot meals are unavailable in about 1,500 schools in England, and children as young as four who are entitled to free meals are given a cold packed lunch.
The estimate was compiled by The TES based on the 21 local authorities which have no area-wide primary school contract for hot meals. Some said all their primaries provide hot meals, with contracts negotiated individually. But in others, hardly any pupils receive a cooked meal. Only two of Dorset's 140 primaries provide a hot meal.
It means they are unlikely to benefit from the pound;280 million announced last week to improve school meals, following TV chef Jamie Oliver's campaign.
Margaret Morrissey, spokeswoman for the National Confederation of Parent Teacher Associations, said young children were often too tired to eat properly after school, so lunch is their most important meal. She said:
"Some of them can't hold a knife and fork. When they go to secondary school, they will just choose a burger and chips that they can eat with their fingers."
Hot meals could cost a primary school up to pound;50,000 where kitchens have been replaced by classrooms, libraries or IT suites, according to the Soil Association.
Labour has promised that some of the pound;6.3 billion Building Schools for the Future programme can be spent on kitchens.
Take part in the discussion on meals at www.tes.co.ukstaffroom