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Parents will be able to drop off children 30 minutes before their usual school time, knowing they will be offered a free breakfast, the government says.
But Association of School and College Leaders general secretary Pepe Di'Iasio said head teachers were "really worried" the basic daily rate of just 60p per pupil was far too low.
"We strongly urge the government to be more realistic about the costs involved, before it attempts to roll out this policy nationally," he said.
The National Association of Head Teachers (NAHT) has welcomed the news but also voiced concern that funding could fall short.
"It will be crucial that these concerns are addressed before the programme is rolled out across the country, to ensure that it does not place further pressure on already strained school budgets," said NAHT general secretary Paul Whiteman.
Announcing the first 750 schools to join the pilot scheme, the Department for Education said breakfast clubs had "an important role to play in the government's commitment to remove the stain of child poverty".
Devon tops the list with 25 schools in the programme, followed by England's largest local authority, Birmingham, with 24.
Both Wales and Scotland have programmes to provide free breakfasts to children in primary schools.
Guidance sent to schools taking part in the pilot scheme says they will receive a set-up payment to cover equipment and material.
Under the scheme, schools will then be reimbursed by the government based on attendance at the clubs - a school with 50% participation in the pilot scheme could get £23,000 a year, the government said.
