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A national version of the scheme was estimated to cost £200 million ($NZ389 million) a year, the report said.
It could be combined with extra study time for children still catching up after schools were closed in the spring.
Some 1.3 million children are eligible for free lunches at schools in England.
The government gave their families food vouchers for the summer school holiday following a campaign by Rashford to provide extra support during the coronavirus crisis.
But last week it voted not to do the same during a weeklong school break at the end of October.
The decision has put pressure on Johnson, who defended the government on Monday.
"We will do everything in our power to make sure that no kid, no child goes hungry this winter during the holidays," he said, describing Rashford's efforts as "terrific".
Adding to the government's embarrassment, businesses and charities across England on Monday offered free meals for children.