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Barbara Sahakian, professor of clinical neuropsychology at Cambridge, said there had been an "explosion" in the number of students taking Modafinil in recent years.

"A lot of young people are purchasing these drugs over the internet, which is a very unsafe way to get these drugs because you don't really know what you're getting and you don't know if it's safe for you as an individual," she said.

She said that some students feel under peer pressure to take the drug in order to keep up with their fellow students, adding: "There's this kind of coercion that goes on.

"I think a lot of students feel it's very unfair that other students are taking these drugs during exams and they feel that they're losing out because the other person has a competitive advantage."

Modafinil is prescribed to treat narcolepsy and other sleep disorders.

It is not illegal for non-suffers to buy prescription-only drugs – with many available online – but supplying them to other people is against the law.

Sky News talked to a number of students at top universities who admitted using the drug, claiming it was widely available on campuses.

Laurie Pycroft, a masters student at Oxford, said: "I have found the ability to go without sleep, when necessary, quite effective. It's essentially like caffeine, just a bit more effective and with less jitters.

"The people I've met who offer me Modafinil for sale, they've all been fellow students, or academic types, rather than your stereotypical wheeler dealer in a hoodie down a dark alley."

Dr Anders Sandberg, research fellow at Oxford's Future of Humanity Institute, claimed to use Modafinil every one or two weeks, adding: "It would be much better if it were in the open market, which would mean that we could actually control that it's actually healthy, that side effects get reported, that you could actually study it properly."

The Medicines and Healthcare products Regulatory Agency said Modafinil should only be taken following a "full consultation with a doctor who can fully assess you for any possible risks associated with taking a medicine".

A spokesman for Universities UK, which represents vice-chancellors, said: "Universities… would have grave concerns about students taking drugs not prescribed to them. Not only is this illegal but it also poses health risks to those students."

An Oxford spokesman said: "If 'cognitive enhancement' drugs are a particular problem at Oxford we have yet to see any substantive evidence for it. We would strongly advise students against taking any drugs that have not been prescribed to them as this could involve putting their health at risk.

"Students who are struggling to cope personally or academically will find a range of support at Oxford."

A spokesman for Cambridge said: "The use of prescription drugs without the approval of a qualified medical practitioner is not to be recommended under any circumstance as unforeseen side effects can be serious."