About two in five students are drug users, says a study from the National Union of Students.
But the students' union argues that students should not be disciplined for "drug-related behaviour that does not constitute a criminal offence".
The most widely used drugs, in a survey of 2,800 students, were cannabis, ecstasy, nitrous oxide and cocaine.
A formal warning was the most common disciplinary action taken by universities over drug use.
The NUS report found drug use to be "a common, although infrequent, behaviour" - with 39% of students using drugs, and cannabis by far the most widely used.
A further 17% had used drugs before, meaning 56% in total had at some time tried them.
Formal warnings escalated
As well as recreational use, there was also a small number of users of "study drugs", intended to keep people concentrating during the exam season.
The report, produced in collaboration with Release, a charity with expertise on drugs and drugs law, argues against a "punitive" approach from university authorities.
Instead of calling the police or imposing punishments for drug-related incidents, the report says students should be given advice and health education.
"Policy responses that focus solely on disciplining students fail to recognise the complex reasons that lead people to use drugs," says the NUS report.
It says there were more than 2,000 incidents last year of "student misconduct for possession of drugs", recorded by universities.
The disciplinary measures were most commonly a formal warning, which could be escalated to a temporary or permanent exclusion.
About a quarter of incidents were reported to police.
There have been rising concerns about mental health problems and student well-being - and this report describes students as often seeing drug use in the context of stress and mental health.
About a third of drug users claimed that they were using drugs to reduce stress - while another third claimed that their mental health was worsened by using drugs.
The report says that for some university authorities, drug use is seen "wholly as a problem to be eradicated through suspensions, evictions and surveillance".
"We believe that these punitive measures rarely help," says the report.
"Instead, they make our educational institutions complicit in practices that prevent marginalised and potentially vulnerable students from seeking help and support."
Sir Anthony Seldon, vice-chancellor of the University of Buckingham, said universities needed to take much greater responsibility for making students aware of the risks of drug use.
"It needs to be made far less socially acceptable. They are profoundly damaging on the minds of the young, especially those with a propensity for mental health problems," he said.
"Drugs wreck people's minds."
He called for tougher action against "pushers who are making money out of the misery of others".
And he called for more education over drugs, in the manner of health campaigns against tobacco, so that students could "make up their own minds".
Professor Steve West, chairman of Universities UK's mental health working group, said: "Universities cannot address drug misuse alone and, working with the NUS, we need to establish closer working partnerships with schools, employers, the NHS and other statutory services to co-ordinate care for students."