Craig Calhoun, director of the London School of Economics and Political Science, and Richard Trainor, principal of King's College London, have complained that it is "impossible" for students to comply with police requirements.
International students have to register with the police within seven days of arriving in the UK or they risk deportation, the letter to the prime minister says.
But they are facing "startling difficulties" in doing so, particularly in London, where only one facility is available, the letter complains.
It follows media reports that hundreds of international students are being forced to queue throughout the night to register at the Overseas Visitors Records Office in south-east London.
"The police are turning away any students who arrive after 6.30am, forcing people to queue overnight...the Metropolitan Policy procedures literally make it impossible for most to comply," professors Calhoun and Trainor say.
"We believe that the present situation is unacceptable and humiliating for the UK higher education sector, and indeed for the country. We hope you will do everything in your power to seek a swift resolution before it escalates into an even greater debacle."
It adds that Malcolm Grant, provost of University College London, has written to David Willetts, the universities and science minister, about the same issue.
The letter is copied in to Mr Willetts and Bernard Hogan-Howe, commissioner of the Metropolitan Police.