Up to 40 colleges hope to introduce special software designed to catch out undergraduates and postgraduates who copy work from the internet.
Universities are also concerned that private tutors are prepared, for a fee, to write essays for students. Practically all degrees contain large elements of course-work which count towards the final degree.
Last week, the Independent on Sunday spoke to tutors who said they would, if paid, write students' essays for them. They claimed buying essays from tutors was common among postgraduate students from abroad, some of whom have a poor grasp of English.
According to one tutor, students are paying around pounds 300 to have their essays written for them. The woman, who did not want to be identified, accused some universities of turning a blind eye to the problem as they sought to increase their income from fees.
"I have been asked to write complete essays and I know this is a very common practice, especially among postgraduate students whose written and spoken English is often not fluent enough to deal with the level of knowledge they are discussing," she said.
"It is common for fashion students who don't even know how to cut their own patterns to go along to the East End sweat shops with large quantities of cash and get their work done for them.
"Some students may not want to come back from their holidays to hand in essays during the summer. They just want to qualify so they will pay someone else to do it for them."
The biggest growth area for cheating is the internet. The revolution in information technology means that students can now download essays and papers from the internet and pass on information by e-mail and computer discs at the touch of a button.
Any computer-literate students wanting, for example, an essay on Jane Austen, can log on to the net and within minutes find an appropriate essay.
Universities are now pinning their hopes of combating dishonesty on anti- plagiarism software developed by Glasgow University.
The software, devised by Dr Rob Irving, a senior lecturer in computing, seeks out structural similarities in students' work. It has already led to 16 students facing disciplinary action for "blatant deception".
Edinburgh University has taken action against more than 117 computer science students accused of plagiarism, and Aberdeen University has disciplined six accountancy students for electronic plagiarism.
And new guidelines for staff produced by Strathclyde University warn that "opportunities for doubtful or dishonest behaviour in submitting assignment for assessment are undoubtedly increasing".
Dr Irving believes the trend towards continuous assessment is a major problem. "There is so much scope for students to copy from each other and get away with it because papers are marked by a great number of tutors," he said.
Some 30 institutions have asked computer consultant David Wools about the anti-cheating programme he has developed.
Mr Wools has worked with experts in forensic linguistics at the University of Birmingham to examine cases of plagiarism in several universities, in subjects ranging from English to business.
His aim is to encourage universities to put in electronic monitoring systems so that students know they are being watched. He has already sold six programmes which look for evidence of collusion in essays through a vocabulary search.
He also uses a second programme to assist in identifying suspect stylistic features in essays. "Not only is the scope for cheating greater but students often have a stronger background in computer use and a higher level of technical competence than those who teach them," he said.
"Programmes like this are designed to counter a problem that has only recently become serious. Many universities are already tackling this, particularly in computer programming, but it needs to become the norm."
However, some problems remain to be solved; Mr Wools pointed out that it was still difficult to protect against students downloading essays from the internet.
Cheating extends to other areas, too. A Liverpool-based entrepreneur, Peter Quinn, is currently under police investigation for selling fake degree certificates on the internet.
The Committee of Vice Chancellors and Principals has obtained an interim injunction to stop Mr Quinn advertising or selling the degrees and to provide the names and addresses of those to whom he has supplied them in the past.Reuse content