Intense competition for graduate jobs means that more than three quarters of employers require at least a 2:1 degree grade, a survey suggests.
The Association of Graduate Recruiters says there are more graduates chasing fewer jobs - with vacancies down by 7%.
Applications have soared, with an average of 69 people chasing each graduate job.
In response, 78% of employers are now filtering out applicants who have not achieved a 2:1 degree.
About two thirds of students achieve either a first class degree or a 2:1 - so this means the remaining third, who will still have passed their exams and paid their tuition fees, will not even be considered by these employers.
"While this approach does aid the sifting process it can rule out promising candidates with the right work skills unnecessarily," says the AGR's chief executive, Carl Gilleard.
"We are encouraging our members to look beyond the degree classification when narrowing down the field of candidates to manageable proportions."
Missing the cut off
The most recent figures - for 2008-09 - show that 64% of students achieved either a first class or upper second degree.
But there are substantial differences within this average. For instance, men are less likely than women to achieve these higher grades and part-time students are less likely to do so than full-time ones.
When these factors are combined, less than half of male part-time students achieve a 2:1 - with this survey suggesting that many will now struggle in the jobs market.
Degree classification was more widely used as a selection criterion than relevant work experience (34%) or degree subject (33%) or going to a particular university (7%).
This annual survey provides a snapshot of the graduate jobs market, based on the experiences of almost 200 leading employers.
It shows that a growing number of graduates are competing for a shrinking number of vacancies.
This has been intensified by graduates from last year still looking for jobs and adding to the pressure on vacancies.
This was the second year of falls in graduate vacancies - and the average number of applicants per vacancy has risen from 49 to 69. Starting salaries remain at £25,000.
This AGR survey, carried out twice a year, concludes that the recovery is "going to be slower than previously thought".
This is the third survey of the graduate jobs market in a week - and taken together they show uncertainty over whether there is a fragile recovery or a continuing decline.
The AGR survey suggests that opportunities for university leavers are getting worse. The current average of 69 applicants for a job contrasts with only 28 in 2006.
But last week, another survey of the graduate jobs market, from High Fliers, found a mixed picture - with a resurgence in vacancies in banking and finance and a decline in vacancies in the public sector.
At the weekend, research from the Higher Education Policy Institute showed that graduate unemployment had risen from 11.1% to 14% - but that it was male graduates in particular who were failing to find jobs.
Such concerns about a tough graduate jobs market comes as a review considers whether universities should be allowed to charge higher tuition fees.
Aaron Porter, president of the National Union of Students, warned that spending cuts could cause even greater difficulties for university leavers.
"We are concerned that the savage cuts to the public sector will create further unemployment, and will make the lives of graduates tougher in an already difficult jobs market," he said.
David Willetts, Minister for Universities and Skills, said: "The job market remains challenging for new graduates, as it does for others. But a degree is still a good investment in the long term, and graduates have a key role to play in helping Britain out of the recession."