Labour says this would improve the health of many young children.
All state school educated pupils in the first three years of primary school already receive free meals, under a scheme introduced by the coalition government.
But Mr Corbyn and shadow education secretary Angela Rayner have proposed extending free meals to all primary pupils.
Mr Corbyn told the BBC:
"No child in the UK should go hungry at school. By charging VAT on private schools fees, Labour will make sure all primary school children, no matter what their background, get a healthy meal at school."
Rob Percival, Senior Policy Officer at Food for Life said:
“Food for Life welcomes this commitment from Labour to providing free school meals to all primary school children. Free school meals benefit every child that receives them, but they benefit less well-off children the most – a universal approach to free school meals in primary schools has the potential to boost overall health and attainment, while alleviating inequalities. The next step for Labour should be a commitment to maintaining and improving the quality of food served, and to maximising take-up through a ‘whole school approach.”