The substance is harmless if left undisturbed, but it can be deadly if it is damaged.
Asbestos is the No. 1 cause of work-related deaths in England, The Guardian reported.
The universities do have asbestos management procedures, but many college representatives said they do not tell students that there is asbestos in their bedrooms.
Students may not report damaged asbestos because they do not know it is there, The Guardian reported.
Of the 88 universities, 38 confirmed that they are providing rooms for students that contain asbestos.
Warwick University said 2,313 of its bedrooms contain asbestos.
"The material containing asbestos in these rooms is fully sealed and completely safe, fully in line with all statutory requirements and good practice," a spokesman from the college said.
The Association of Teachers and Lecturers said it is concerned about the findings.
"ATL has campaigned hard for a national audit to check for the presence and state of asbestos in all education establishments and for its safe removal. This discovery shows how necessary and urgent this is," a spokesman said.