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.
And the stiff competition for young people starts long before embarking on a degree course, with the high number of sixth formers achieving high grades making the fight for a university place even tougher.
Research commissioned by ACS International Schools suggests university admissions officers are struggling to identify the best students because of "inflated" A-level grades.
The survey of 40 UK admissions officers and 20 from the United States found 53% thought "grade inflation" made spotting the best candidates harder.
Last year, more than one in four A-level exam entries (26.7%) were awarded an A grade.
Concerns about a tough jobs market for graduates 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."
Graduates from across the UK have been sharing their experiences with BBC Online. Here is a selection of their comments.
I have recently graduated with a 2:1 but I have been unable to apply for the majority of graduate schemes as employers are demanding high A-Level results. I feel that this is unfair.
Jessica McKinven, Doncaster, England
I graduated last year with a first class masters degree in civil and structural engineering from the University of Liverpool. Following graduation I decided to take a gap year and spent the winter working in a ski resort in France. Having returned from France, I found the graduate job market in a far worse state than when I left. This is a terrible time to be a graduate. If the situation does not change for the better soon, I will be looking for greener pastures abroad.
Marc Atherton, Warrington, England
Considering the domestic economic climate, the amount of students now going to university in the UK and the increasing emergence of a global labour market, it is not surprising that employers are demanding more and more from graduates. I have decided to move to China on completion of my masters in September, gain industry experience (where there are opportunities) and learn Mandarin to further differentiate my CV from my competitors.
James, Welwyn Garden City, England
It's bad for graduates in the UK but it's even worse for international students. It is next to impossible to find a job after spending close to £50,000 on a degree - there's always a problem with getting a job with a post study work visa. I am ashamed to say that I was fooled into coming to England to progress in life and like many other educated people I am fleeing this country for better opportunities.
Malintha Delpachitra, Southampton, Hampshire, England
I graduated with a 2:2 but this was partly due to a dissertation problem, based on all other results I would have achieved a 2:1. Now, a year on after graduating, I'm still looking for a job. I have to rule out most jobs I look at due to the 2:1 requirement. I have six years management experience as well as my degree but apparently I'm unsuitable because of my 2:2.
Paul Donnelly, Glasgow, Scotland
I graduated with a BSc (Hons) 2:2 and went on to do an MSc at Imperial College from which I graduated with distinction. This was still not enough to be considered for many research posts and jobs.
Elena, London, England
As a 2009 graduate I have found that the graduate job market is practically closed to anyone other than those already working in the same or similar roles as those available. However, on the plus side, Britain has an extremely well educated customer service and retail industry!
Bern, Coventry, England
What's so bad with doing well at university? I know I strive to get a first. If you are paying for your fees like you do in England, you should be putting in the effort. Thankfully I do not have to pay my tuition fees, but I still put in a lot of effort. If the students are not achieving at university, how can employers expect them to perform well?
As a university careers adviser, I try to help students and graduates understand the full range of opportunities they can consider. Management training schemes are great opportunities for graduates, but not everybody wants or is suited to a life in the corporate world. Let's not forget the thousands of small and medium-sized employers across all industries and sectors.
Alexandra Hemingway, Guildford, England
A warning for graduates thinking that they can wait until we're out of the recession before looking for a graduate job. When I was looking for jobs a few years ago, I found that many employers would automatically reject graduate scheme applicants who had been out of university for more than three years.
Rachel B, Leeds, England
Picking a tough course at a tough university was foolish and not worth the risk. The vast majority of graduate jobs have told me not to bother applying unless I have a 2:1. Knowing this now, I would have gone to a mediocre University and studied a far less challenging degree.