Vocational exams, including BTEcs, are to go ahead this month in England - despite calls for them to be cancelled alongside GCSEs and A-levels.
"Schools and colleges can continue with the vocational and technical exams that are due to take place in January, where they judge it right to do so," said a Department for Education spokeswoman.
Further education college leaders had complained this was unfair to students.
They said students would face "stress" from taking exams in the lockdown.
The Association of Colleges warned the decision, giving schools and colleges the option on whether to carry on with BTecs, would create more confusion.
Chief executive David Hughes said some colleges would cancel exams and others would continue - but without any clarity about what would happen to "students in colleges which do cancel for safety reasons".
"A national decision would have allowed for more fairness," said Mr Hughes.
The announcement from the Department for Education has left it open for schools and colleges to decide whether to go ahead with vocational and technical exams.
"Schools and colleges have already implemented extensive protective measures to make them as safe as possible," said the DFE's spokeswoman.
The Department for Education said it recognised "this is a difficult time" but wanted to allow students who had prepared for exams and assessments to continue, including those who needed to take hands-on practical tests for qualifications for jobs.
A joint statement from the mayors of Manchester and Liverpool said it was wrong to go ahead with these vocational exams when other academic exams had been cancelled.
"It is unfair to ask these students to go into colleges when everyone else is being told to stay at home.
"This will cause unnecessary anxiety and concern just when they need to be able to focus," said the statement from Andy Burnham and Steve Rotheram.
The mayors highlighted that students taking BTecs were more likely to be from "working-class backgrounds and ethnic minority communities" and they should not be treated any less well than those following an "academic route" in exams.
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