In a third area, means testing for free meals will be altered so that more pupils qualify.
The government, education authorities and primary care trusts will share the £40m cost.
A number of areas have already tried a variety of similar ideas. Unions have pushed for universal entitlement, with a cost estimated at £1bn a year.
The Scottish government is about to decide whether to give free meals to infant pupils, after a year-long pilot in five areas.
England's national trial scheme would start in a year's time and run for two years, with what ministers say would be a rigorous evaluation.
This would look at the benefits in terms of increased uptake of healthy meals and children's behaviour, obesity and general health and well-being.
It is not yet known which areas would be involved but the trial would be funded to the tune of £10m apiece by the health and schools departments, who want to see matched funding from local authorities and primary care trusts.
