Students at the University of Leeds are calling for anonymous marking of all students' work after it emerged this week that some departments think the procedure is impractical.
Emma Rabin, Leeds students union education officer, said students were pleased that the university senate had recently agreed to make anonymous marking compulsory from next academic year.
But she said students wanted the university to introduce the policy for all assessed work as well.
Ms Rabin said: "Currently departments have the option of marking exams anonymously and some have said the procedure is impractical and time consuming. Unfortunately, many students assume their work is anonymously marked and when they find out it is not, they get upset."
Ms Rabin said that some unconscious bias was bound to creep into marking.
"We are asking for this as a safeguard for staff as well as students," she said.
The National Union of Students said it was planning to step up its campaign for a universal system of anonymous marking in September.
NUS education officer Richard Darlington said:. "We would like all marking to be anonymous whether for exams or assessed work. This is not saying that academics are racist or sexist, it is simply acknowledging that subconscious bias is an inevitability unless safeguards are put in place."
The NUS said research earlier this year showed that at a London University, black students' marks were 4.2 per cent lower than those of white students. In Scotland, only 20 per cent of the students on one course were Asian but 80 per cent of those who failed were Asian.
The NUS said that where anonymous marking had been introduced, many of these disparities had disappeared.