The University of Glasgow's student council is calling for a cap on numbers over claims the student population has grown 40% in just five years.
It said 10,000 additional students had put a strain on accommodation and was damaging their welfare and the quality of education.
But the university said there was not a "significant negative impact".
It comes after new students were told by the university they could not be guaranteed accommodation this year.
The university blamed increased demand and a "significant contraction" in Glasgow's private rental market.
