A "major financial house" has specified in an advert placed with information technology recruitment consultancy Computer Futures that candidates must be "redbrick graduates".
The advert, on their website, was for a data and systems manager. It said the redbrick graduate must be ambitious but that no experience was needed.
A spokesman for the Higher Education Funding Council for England said: "To advertise in this way is to close off opportunities to a major sector of very gifted and able graduates."
A spokesperson for the consultancy said: "How we advertise our jobs depends on the clients' requirements."
Peter Prince, deputy director of the school of computing and maths at the University of Teesside, said: "There is still prejudice against new universities; it takes at least ten years to break down the barriers."