Labour’s motion, which called for the scheme to be extended over school holidays until Easter 2021, was defeated by 261 votes to 322 – majority 61 - on Wednesday, October 21.
Following the vote, Manchester United forward Rashford vowed to continue campaigning, writing on Twitter: “For as long as they don’t have a voice, they will have mine.”
Since then, hundreds of businesses across the country have come forward to offer free meals - including Indian restaurant Mumtaz, in Leeds Dock.
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Schoolchildren aged between four and sixteen will be able to get a free chicken or vegetable biryani from the Chadwick Street restaurant from Saturday October 24 until Sunday, November 1.
The hours to pick up the food are between 5pm and 6pm.
Mumtaz asks that children under 12 come with an adult.
Posting on Facebook, a Mumtaz spokesman said: "We will help if the MP's wont. Put politics to the side.
"No child should go hungry during half-term.
"We are doing this to do our part to support young children and families who truly need support.
"We are all struggling but sometimes the answer is to be be grateful and help more."
Mumtaz, which was founded in Great Horton Road in Bradford back in 1979, is now urging other Leeds businesses to follow suit and offer free meals this half term.
The co-owner of Mumtaz, Asad Arif, said: "This is NOT about politics. This is about doing our part to help.
"If you are a business owner, please do consider doing this yourself. Good only begets good.
"We have to help each other during these very difficult times.”
Five of Leeds' eight MPs voted for the motion including; Leeds Central MP Hilary Benn, Leeds East MP Richard Burgon, Leeds North East MP Fabian Hamilton, Leeds North West MP Alex Sobel and Leeds West MP Rachel Reeves.
Morley and Outwood MP Andrea Jenkyns, Elmet and Rothwell MP Alec Shelbrooke and Pudsey MP Stuart Andrew voted against the motion.
Hilary Benn, who represents Leeds Central, said the outcome was "absolutely shameful" but the public support for the campaign would drive it forwards.
He said: "It was absolutely shameful of the Tories to vote against free school meals being provided over the holidays. How on earth can they justify it?
"Boris Johnson now needs to explain to 25,000 children from low income families in our city why they won’t be getting the help that would make such a difference to them and to their parents at time when many families are struggling?
"We won't, however, be giving up. There is huge public support for this campaign."
Rachel Reeves, MP for Leeds West added that "sink-or-swim" plans for support could leave more than one million children at risk of going hungry over the school holidays and urged the Prime Minister to re-think.
The Local Government Association Labour Group with increased lockdown restrictions but without free school meals.