University lecturers are warning that they do not want to become "immigration officers" in the enforcement of tougher rules on student visas.
"We have grave concerns that new rules on monitoring foreign students have been pulled together without any consultation with the people who would be tasked with their implementation," says Ms Hunt - who is one of 200 signatories to a letter protesting against the plans.
"We do not believe it is appropriate or effective to task colleges and universities with the policing of immigration," she says.
The union has previously opposed suggestions that university staff should identify students who might pose a security threat.
"As we said then, if people wanted to go into the monitoring or spying game they would have become spooks," she says.
The letter, sent to the Guardian newspaper, says: "This police-like surveillance is not the function of universities, and alters the educational relationship between students and their teachers in a very harmful manner."