OXFORD City Council is considering stopping 'directly providing events' - such as policing May Day morning and organising the Lord Mayor's Parade - in a bid to save money.
The authority is trying to cut more than £5m from next year's budget.
Although May Morning is not an 'official' event, the city pools resources with the county council and emergency services to marshal the occasion.
This year the council spent almost £6,000 paying for a line of 30 marshalls to stop jumping from Magdalen Bridge.
It is unclear how next May's event would be coordinated. Police want the bridge closed.
City council leaders estimated that pulling out of May Morning and organising the Lord Mayor's Parade would save £71,000.
Lord Mayor John Tanner said there was no point in having a Lord Mayor unless they were able to be active.
He added: "The parade doesn't have to cost that much at all.
"As far as May Morning is concerned, I've always thought that public protection should be provided by the police and Magdalen College - I don't see why the city has got to get involved."
A city council spokesman said: "No decisions will be taken until February next year when the budget is finalised."
Oxford police declined to comment.
Magdalen College bursar Mark Blandford-Baker added: "The college is not involved with what happens out on the public highway, so I am not in a position to comment."
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