Students at prestigious universities have been turned away from overcrowded lectures and told to watch classes online or in overflow rooms.

The Observer found that students paying £9,250 or more in Manchester, Nottingham and Lancaster, had struggled to get a seat in lectures. Manchester University maths students in a 600-capacity hall were given slips with a link to a YouTube live stream and told they could “sit in a coffee shop” and watch. They were also given the option of sitting in a separate overflow theatre to watch the stream, without being able to participate or question lecturers.

Last October, the University of Nottingham advertised a £9.65-an-hour role for a temporary worker to monitor the overflow live stream for first-year law students. In November, psychology students at the University of Lancaster were sent to overflow rooms and given the option to watch lessons on their laptops because lecture theatres were full..

Overflow rooms typically accommodate large audiences when well-known figures give public lectures. All the named universities said that overflow classes were a short-term arrangement to cover busy periods at the beginning of the academic year.

Sofija (who declined to give her surname), a student at the University of Manchester who attended the maths lecture, told the Observer that she saw people being turned away. The economics undergraduate decided to stop going to the class because it was so difficult to concentrate.

“Even if you were in the lecture and got a seat, it was literally impossible to pay attention,” she said. “I’ve got an anxiety disorder, which gives me some sensory issues, it was 100% impossible for me to pay attention or learn anything. I did not go to the lectures, I had to watch them online.”

The National Union of Students, which represents higher education students, said that packed lectures were a result of “desperate” universities being forced to bring in as much tuition-fee income as possible.

In a separate example of overcrowding, a physics lecture at King’s College London, one of 24 universities in the elite Russell Group, was reportedly so busy that students were told to “cram” in, with some standing at the back.

Julio Figueroa, an international student from Mexico who pays more than £25,000 a year to study at King’s College London, said that he had to take his own chair into a physics lecture on at least two occasions. “We are in a Russell Group university, I feel like this shouldn’t happen,” he said.

There is no evidence of the university running overflow lectures, and it said it had no knowledge of students taking their own chairs into lectures.

Universities UK, which represents higher education providers, said it was important that all students could access lectures. “Universities will be mindful to ensure this does not compromise the quality of teaching or disadvantage students not attending in person. There is no indication of common or continuing issues with students being asked to join overflow or online lectures against their wishes,” a spokesperson said.

The University of Manchester said that the maths overflow was temporary. “When overcrowding does occur, we work with schools to resolve it as quickly as possible and use various solutions, including moving the lecture to a larger location or splitting the cohort into smaller groups.”

Nottingham said its overflow lecture was the result of a timetabling problem that affected a small number of students. “For a two-week period last September, a particular set of law lectures proved more popular than anticipated for the allocated theatre capacity,” it said. “Rather than disappoint students, we arranged a live stream of the lecture for some 20 students in the adjoining theatre, with full technical support and additional tutorials to ensure they could explore the lecture topic in person with tutors.”

Lancaster said it had run overflow lectures owing to the popularity of its course. “There is always a staff member present in the streamed venue and there are mechanisms in place so students can ask questions.”