One opponent to Rashford's plea was newspaper columnist and former reality television contestant Katie Hopkins.
"I look hot in blue. Just saying," Hopkins tweeted with an image of her head on a Manchester City player's head.
The official Twitter account of the Premier League champions replied: "Not in our blue. Just saying!"
Johnson's spokesman, James Slack, said "the prime minister fully understands that children and parents face an entirely unprecedented situation" because of the coronavirus pandemic and nationwide lockdown.
After the announcement Rashford tweeted: "I don't even know what to say. Just look at what we can do when we come together, THIS is England in 2020."
Johnson said he had spoken to Rashford to congratulate and thank him.
"We have to understand the pressures families are under right now and that's why we've responded as we have," Johnson said.
The athlete wrote an open letter to all of Britain's lawmakers on Sunday, describing how, as one of five children of a hard-working single mother, "we relied on breakfast clubs, free school meals, and the kind actions of neighbors and coaches."
"A a black man from a low-income family in Wythenshawe, Manchester, I could have been just another statistic," he wrote. "Instead, due to the selfless actions of my mum, my family, my neighbors, and my coaches, the only stats I'm associated with are goals, appearances and caps. I would be doing myself, my family and my community an injustice if I didn't stand here today with my voice and my platform and ask you for help."
When schools were shut down in March as part of a nationwide coronavirus lockdown, a food voucher program was set up to help ensure they didn't go hungry. Vouchers worth 15 pounds ($19) were given to spend each week in supermarkets.
The government now says it will continue the voucher program over the summer in England at a cost of 120 million pounds ($152 million). Authorities in Scotland and Wales have similar plans.
Until Tuesday, Johnson's Conservative government had refused to budge, pointing out that it has earmarked an extra 63 million pounds ($80 million) for local authorities to support vulnerable families.
But Rashford's campaign quickly picked up steam, backed by celebrities, opposition politicians and some Conservative lawmakers nervous that the government was appearing impervious to the struggles faced by many British families during a pandemic in which millions have lost income or jobs.
Conservative legislator Robert Halfon, who chairs Parliament's education committee, said after three months of a lockdown that has seen the British economy shrink by over 20% "so many people up and down the country are struggling to keep a roof over their heads and to feed their families."
The government is already facing intense criticism for its response to the coronavirus pandemic. Britain's official death toll of almost 42,000 is the highest in Europe, and the government has been accused of putting the country into lockdown too late, costing thousands of lives, and having inadequate stocks of protective equipment.
Johnson — who was hospitalized with the coronavirus in April — has performed a series of policy zigzags during the outbreak. Last month the government said it would stop charging foreign medics and care workers to use the health system. And on Tuesday it released a report on the factors behind COVID-19's disproportionate impact on ethnic minority communities that it had previously withheld.
Rashford's achievement in forcing the policy change drew praise from the words of sports and politics.
Anne Longfield, England's children's commissioner, thanked Rashford for highlighting "the blight of holiday hunger."
Manchester United's official Twitter account said: "A hero. An inspiration. One of our own. We are so proud of you, @MarcusRashford."
Premier League chief executive Richard Masters praised Rashford's perseverance.
"It's a really important and heart-moving cause so I offer my congratulations to him," Masters said.
In a statement, Rashford thanked British lawmakers for listening.
"This was never about me or you, this was never about politics, this was a cry out for help from vulnerable parents all over the country and I simply provided a platform for their voices to be heard," he wrote. "I stand proud today knowing that we have listened, and we have done what is right. "
