Covered Market traders want Oxford University police stripped of their powers.
Traders have written to Dr Evan Harris, MP for Oxford West and Abingdon, asking for an amendment to a Police Reform Bill currently going through Parliament that would remove powers enjoyed by the University Police since 1825.
The police, known as Bulldogs, have the same powers as police constables, including the power of arrest, within four miles of any university building.
A dispute arose after university police demanded traders move delivery vehicles in Merton Street to allow room for students leaving the Examination Schools.
Alan Lester, a traders' spokesman, said: "These people are an anachronism. They've no responsibility for us or over us but they claim that they do.
"They're not accountable to any public authority. We want an amendment put into the bill that excludes them from having any lawful authority over people who are not members of the university."
The University Marshal, Richard Hartley is reviewing their duties and management structure.
A university spokesman said: "The University Police work to ensure staff and student safety and discipline at the University of Oxford.
"Its trained officers are required to comply fully with existing law and the University Police has worked closely alongside Thames Valley Police for many years."
Dr Harris said he did not know if an amendment would be "within the scope of the Bill".
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