The government is "disguising the extent of of graduate over-qualification", according to the CIPD, the professional body for HR and people development.

Earlier this week, Universities Minister Jo Johnson said in a speech that "official statistics show that in fact only 20% of recent graduates did not find a graduate level jobs within three years of leaving college".

The Minister went on to suggest that statistics from new CIPD research showing that about 58% of UK graduates were in non-graduate jobs exaggerated the problem.

Now, the CIPD has hit back. Along with independent education charity the Edge Foundation, it said that the Higher Education Statistics Agency figures cited by the Minister are misleading and not relevant to the debate about graduate over-qualification.

David Harbourne, acting chief executive of the Edge Foundation, said: "The same official statistics cited by the Universities Minister show that, after accounting for non-working graduates, around half of all 2011 graduates failed to get a graduate-level job within three-and-a-half-years of completing their degree. And this is an average figure: for people with arts, humanities and social science degrees, the situation is significantly worse. The uncomfortable truth is that vast numbers of graduates struggle to get onto the professional career ladder when they leave university.

"In addition, many of these 'graduate level' jobs in the official statistics can be accessed by people without degrees, who have vocational qualifications or who have worked their way up via an apprenticeship."

Peter Cheese, chief executive of the CIPD, said: "We stand by our recent research report, 'Over-qualification and skills mismatch in the graduate labour market', shines a light on the extent of graduate over-qualification in the UK labour market and received widespread support for the issues raised. It shows that around 58% of UK graduates are in non-graduate jobs, a very high proportion by international standards, and that if you compare graduates to non-graduates doing the same job in the majority of instances there is no resultant change to the skills requirement for that role. Simply increasing the qualification level of individuals going into a job doesn't typically result in the skills required to do the job being enhanced - in many cases that skills premium, if it exists at all, is simply wasted."