The firms insist that they do not aim to help cheats when they offer GCSE, A-level and university assignments for sale over the web. Now the boards want the firms to make cheating using the essays they sell impossible - by handing over copies. These can then be fed into a computer database to allow any plagiarism to be detected.

Barclay Littlewood, owner of the most prominent essay sales website, said his firm was considering the move and that he has been calling for years for more regulation of the burgeoning industry.

Thousands of students are obtaining coursework from sites, that either offer assignments already submitted by other students, or “bespoke” pieces written to order by graduates. Companies such as Mr Littlewood’s, however, insist that the coursework is offered merely to help students with their studies and that it should never be submitted by them for exam grading.

Ellie Johnson Searle, chief executive of the Joint Council for Qualifications, the boards’ umbrella body, said: “This is all about ensuring the integrity of GCSEs and A-levels. We are looking at persuading the people running these sites to give us the essays, if they are so confident that the coursework they offer is not going to be submitted (for a grade).

“We can then put them into Turnitin (an anti-cheating database) to check against plagiarism.”

Ms Johnson Searle said that if the companies were genuine in their claims, they should have no problem with co-operating.

The JCQ has not yet held talks with the firms. But Mr Littlewood, who runs ukessays.com, said that he would take the challenge seriously. He said:

“That’s the sort of solution that we should be looking at.”

He said universities should consider the same move. However, he also wants universities to respond by stopping advising students to avoid sites such as his.

The JCQ has also written to eBay, the online auction provider, to urge it to take GCSE and A-level essays off its site. Managers at eBay are still considering how to respond.

The TES revealed last year how essays and scientific investigations have been on sale on eBay for as little as 99p each. This week, a selection of assignments were on offer.

Plagiarism concerns partly explain the Qualifications and Curriculum Authority’s proposal to replace coursework in many subjects with supervised in-class tests within years.