The England and Manchester United star, along with child poverty campaigners, were celebrating after the Government said it would now provide free meals to disadvantaged children
The Prime Minister personally phoned Rashford after he played in his team’s Premier League clash against Everton on Saturday to alert him to the decision to lay on £170 million of extra funding for the measure.
The money will pay for the Covid Winter Grant Scheme to support families over the season while the Holiday Activities and Food programme will be extended to cover the Easter, summer and Christmas breaks in 2021, the Department for Work and Pensions (DWP) announced.
But Leeds City Council's executive member for learning, skills, employment and equality, Jonathan Pryor, said the Government needed to do more.
"While this U-turn from the Government is welcome, and I thank the Prime Minister for finally listening to the outcries from families, councils, charities, businesses, schools and of course Marcus Rashford, this only serves to demonstrate how little of a plan the Government has to get us through the Covid crisis," he said.
"It additionally shows how a decade of cuts from the Conservatives have left the country in such a state that we need emergency measures such as this to ensure children are fed.
"We are now calling on the Government to address why so many children in our country, one of the wealthiest countries in the world, are living in poverty."
As part of the new package, Healthy Start payments, which help expectant mothers and those with young children on low incomes and in receipt of benefits to buy fresh fruit and vegetables, are set to rise from £3.10 to £4.25 a week from April 2021.
Making the announcement, Work and Pensions Secretary Therese Coffey said: “We want to make sure vulnerable people feel cared for throughout this difficult time and, above all, no one should go hungry or be unable to pay their bills this winter.”
Coun Pryor added: "In the coming days we will be looking through the detail of exactly what the Government is offering Leeds, and using whatever we’re given to protect the most vulnerable in our city.
"Over the last half term it was left to the generosity of our own community and squeezing already stripped Council budgets to do the right thing.
"Councils are at the forefront of the fight against Covid, and the Government is forcing us to cut budgets while we do our part in fighting this pandemic.
"This is unbelievably short sighted, counter productive, and will simply cost more in the long run.
"I hope the Government reflect on this wider point in the coming days and weeks."
The U-turn comes after the Government last month whipped Conservative MPs to vote against a Labour motion in the House of Commons calling for the extension of free school meal provision following Rashford’s campaign.
Businesses and councils across Leeds stepped into the breach following the result, announcing they would fund meals during the October half-term for those who needed them.
The DWP confirmed the new £170 million worth of winter grants would be administered by councils in England rather than schools.
The funding will be ring-fenced, with at least 80 per cent earmarked to support with food and bills, and will cover until the end of March.
Local authorities will receive the funding at the beginning of December.
Rashford said he was “so proud” of those who had united behind his campaign and that he was “overwhelmed by the outpouring of empathy and understanding”, promising his supporters to “fight for the rest of my life” to end child hunger in the UK.