Milk subsidies for 1.3 million children in 12,000 English nursery and primary schools are to continue despite warnings that they are a waste of money.

Ministers who are trying to improve nutrition in food and drink available in schools were reluctant to sanction changes that might appear to undermine their health drive and send the wrong signals about the government's commitment to the dairy industry.

London Economics, the consultancy hired by the government, had said the £1.5m-a-year top-up to European Union subsidies for the scheme was excessive and did little to improve health. Parents were still paying on average 11.4p for a third of a pint (just under 200 millilitres) of milk - far more than the price in supermarkets.

But Lord Bach, the minister for sustainable food and farming, said he and health and education ministers had considered "all relevant factors" in deciding not to scrap the top-up payments. "We have agreed the scheme has a valuable role to play."

Stephanie Spiers, chair of the charity Milk for Schools, said: "Common sense has prevailed. We would like things to go further. We would also like a targeted [free] milk scheme that worked properly." Councils taking up subsidies were obliged to provide free milk for children with parents on income support and others entitled to free school meals, she said, but no one monitored how widely that occurred. Provision was better in Wales and Scotland.

The decision was also welcomed by the dairy industry. "The effect of ending this subsidy would have been to deprive needy children of the nutritional benefits of milk," said Jim Begg, director general of Dairy UK.