The education secretary, Damian Hinds, has called on university students to report their peers if they suspect them of cheating as part of a government crackdown on essay writing services.

Students who are found guilty should face severe consequences, he said, including being kicked off their courses. He urged universities to get their students to sign “honour codes”, making a pledge not to cheat.

Universities and government ministers have become increasingly concerned about a growing market in essay-writing services, known as essay mills, which offer bespoke pieces of work – for a fee – that are virtually impossible to detect through anti-plagiarism software.

Hinds encouraged students to come forward to act as whistleblowers, saying: “Nobody likes the idea of telling on your school friends or peer group but actually there should be a culture that says it’s not OK to cheat.”

Some vice-chancellors have called for the essay-writing companies to be banned as they have been elsewhere in the world. The government has not ruled out legislation, but the education secretary said many companies operated overseas, making it difficult to act against them.

The companies recruit students by advertising their services heavily online. A number of tech firms including Google and YouTube have already taken steps to remove hundreds of advertisements and promotional material on their sites, but the education secretary said others had not followed suit.

He cited PayPal in particular, urging the company to stop processing payments to essay-writing companies. “I am determined to beat the cheats who threaten the integrity of our system and am calling on online giants, such as PayPal, to block payments or end the advertisement of these services. It is their moral duty to do so.

“There has been some positive progress made by some in the tech sector but it is vital that we all unite to clamp down on this practice and the companies that are feeding on it.”

PayPal declined to comment on the education secretary’s intervention but a spokesperson confirmed that a review on this issue was already under way.

The true scale of cheating is unknown, but new technology has made an old problem considerably easier. In 2016, the higher education standards body, the Quality Assurance Agency (QAA) found about 17,000 instances of cheating per year in the UK, but the number of students using essay-writing services is thought to be higher as customised essays are hard to detect. A study by Swansea University found one in seven students internationally have paid for someone to write their assignments.

Universities UK (UUK), the collective voice for 138 universities, has called for essay mills to be made illegal. Chris Hale, the UUK director of policy, said: “All universities have codes of conduct that include severe penalties for students found to be submitting work that is not their own. Such academic misconduct is a breach of an institution’s disciplinary regulations and can result in students, in serious cases, being expelled from the university.

“Universities have become increasingly experienced at dealing with such issues and are engaging with students from day one to underline the implications of cheating and how it can be avoided.”