The University of Cambridge is facing calls for students to be able to retake their final year, after the coronavirus caused exams to be cancelled.
An open letter to education pro-vice chancellor Graham Virgo warns that remote learning could affect academic performance and student wellbeing.
Those without adequate resources at home will suffer, the letter reads.
It follows an appeal by the vice-chancellor Stephen Toope, who urged all students to "return home now".
The letter, signed by more than 1,300 undergraduates so far, says students will face "myriad challenges" during the coronavirus restrictions, including the possible need to care for ill relatives, self-isolation, and "negotiating complex and changeable immigration policies".
"Marginalised and less privileged" students, like the disabled, would be likely to be worst affected, it adds.
It suggests a choice of scheduled paper exams, or predicted marks "based on supervision reports", as well as the option to restart the year in September, or retake the Easter term in 2021.
"We appreciate the impossibly difficult situation presented to the university," the letter reads.
"We write to you hoping to be part of the solution."
The letter adds: "We do not want to feel compelled to make the difficult choice between our health and that of our loved ones and communities on the one hand, or our future careers on the other."
A coronavirus update on the students' union website (CUSU) says: "We have stressed our opposition to assessments being carried out online in strict timed conditions and have urged the university to adopt as much flexibility as possible in developing these alternative arrangements."
On Wednesday, Prof Toope announced that all examinations had been cancelled - with face-to-face teaching moving to online platforms.
He urged international students to make immediate travel arrangements to return home.
"We are all facing an unprecedented crisis," he wrote, adding: "It may be months before we resume normal activity."
The university has more than 23,000 students, of whom more than 40% are from other countries.