The council funding will ensure schools have the kitchen facilities and equipment needed to support the increased number of hot meals served.
Sadiq Khan, who received free school meals as a child, has stepped forward with an emergency £135m to help 270,000 primary schoolchildren in London receive free school meals from September 2023 for one year.
Cllr Penny Frost, chair of the council's education and children's service committee said: "We have welcomed the expansion of the free school meals provision to all primary children for the next academic year, at a time when many families are feeling the impact of high food prices and the cost of living crisis. Good nutrition is essential for physical and mental wellbeing and development, and we know that children learn better when they are well fed.
"We anticipate that this offer will be popular and one that parents will hope to see extended beyond a year. Our schools have had to make a significant capital investment to deliver meals for this coming year so if the offer continues, which we hope it will, it will be critical that the Mayor and the Department for Education work to release funding for ongoing costs."
Richmond Council is also continuing to provide school meal vouchers for the borough's lowest-income families over the school summer holidays. Each eligible child is receiving £120 for the six-week school holiday period, which is £30 more than was provided last year.