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The motion was put forward at the weekly student council, which heard how meat can impact climate emissions, and how greenhouse gas emissions disproportionately affect developing countries.
The union itself cannot change university policy - as it exists only to represent students in the university's decision-making processes - meaning executives will now lobby the institution to introduce the meat ban on campus, including eateries in libraries and other university buildings.
The motion said: "As the UK's premier university, the nation looks to Oxford for leadership, but Oxford has shown a lack of leadership in addressing climate change.
"The banning of beef and lamb at university-catered events and outlets is a feasible and effective strategy to help the university meet its revised 2030 goal."
The motion does not affect the university colleges, where students live and have tutorials, as these are treated separately and must decide on their stance individually.
However, students believe the proposed ban could lead to further changes elsewhere.
"A change at the university level will open the gates for similar change at the college level," the motion said.
"The university has a commitment to anti-racism, and this requires urgent action to minimise greenhouse emissions."
The motion, written by Vihan Jain, Daniel Grimmer, and Agatha Edevane, passed with 31 votes for and nine against, with 13 having abstained from voting.
It is part of the University's sustainability drive, with aims to cut its carbon emissions by 50 percent by 2030.
Ben Farmer, representing charities and the community at the Oxford Students' Union, said: "I welcome the mandate to engage the university on this important issue.
"It is important to recognise that food-based changes may not be possible for every student or staff member at the university.
"Further, food-based changes are just one part of changes we'd like to see the university make to tackle the climate crisis."
If Oxford University does end up changing its policy, it would follow other institutions including Cambridge University and Goldsmiths University in south-east London, both of which have already banned beef from campus.
LADbible has contacted Oxford University for comment.
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