It's claimed the move will deplete services in some of the city's most deprived areas.
Excellent Research At Scots Universities
Scottish universities are producing "world leading'' research across a range of subjects, according to an in-depth report.
Rankings show that Edinburgh is fourth in the UK behind Oxford, University College London and Cambridge in terms of research.
Glasgow, St Andrews and Strathclyde are also in the top 30 produced by Research Fortnight, based on the results of 2014 Research Excellence Framework (REF), a large-scale exercise which reviews the quality of research in different subjects at universities across the UK.
Subjects such as chemistry, biology, physics, history and art and design are particularly strong in Scottish research.
In total, the research of more than 52,000 academic staff working at 154 institutions was peer-reviewed by a series of expert panels.
They graded the work, giving the best 4* (world leading) down to 1* (recognised nationally). The study was last carried out in 2008 and the latest results will be used to allocate research funding of around £2 billion a year to universities from 2015/16.
Together, Scottish universities submitted research to all 36 assessment units and achieved "world leading'' status in each.
More than 75% of Scottish research submitted to the REF2014 was judged to be ``world-leading'' or internationally excellent overall, according to Universities Scotland, the representative body for higher education in the country.
Professor Pete Downes, convener of Universities Scotland and principal of the University of Dundee, said: "The new measure of the impact of university research will be of particular interest to politicians and the public as this has assessed what wider economic, social or cultural contribution university research has.
"I couldn't be any prouder that Scotland's universities have been shown to excel in the impact of their research with over 85% being found to have had either outstanding or very considerable impact, a performance which is significantly better than the average across the UK.''
The University of Edinburgh's research in sociology, environmental sciences and computer science and informatics was rated the best in the UK, based on the breadth and quality of research.
Joint research submissions with Heriot-Watt University in maths was rated fifth in the rankings, while Edinburgh and the University of St Andrews placed second for a joint submission in chemistry, and fifth for a submission in physics.
Edinburgh principal Professor Sir Timothy O'Shea said: "Research at the University of Edinburgh is constantly expanding the depth of human knowledge and making an impact on the wider world - whether it be improving the effectiveness of youth justice policy and practice, or shaping the technologies used to manage the world's data.
"Our outstanding researchers enable us to forge links with charities, businesses, policy makers and other universities, so that together we can tackle long-standing challenges at home and overseas.''
The University of Glasgow was rated second in Scotland for research and 12th overall in the UK.
Principal and vice-chancellor Professor Anton Muscatelli said: "It is particularly pleasing that, in line with the aspirations of the university set out in the university's 2020 Global Vision, 31% of our output was judged to be of 'world-leading' quality.
"This success lies at the very heart of our contribution to the UK's economy and, in particular, Scotland's economy.''
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