People have been injured jumping off the bridge in the past
Local councils and the emergency services have combined to reject claims that closing Oxford's Magdalen Bridge on May Morning costs money.
The bridge has been closed for the past three years during the traditional celebrations to stop people jumping from it into the river below.
Oxford City Council said managing the event costs it £6,000 whether the bridge is open or closed.
It said it was a myth that closing the bridge costs the public money.
Michael Newman from the council said: "With such a large gathering of people, officers from the police and city and county councils would always need to be present.
"There would be cost for those authorities regardless of whether the bridge was opened or closed."
In 2005 the ambulance service said treating those injured after they jumped from the bridge cost it £50,000.