The British government has been urged to outlaw essay writing services that allow university students to pay for coursework for their degrees, after a study found that use of “contract cheating” is rapidly increasing around the world.

The study by Prof Philip Newton at Swansea University’s medical school collected evidence from surveys taken among students in higher education, and calculated that as many as one in seven recent students internationally have paid for someone to produce their assignments, potentially representing 31 million students.

While there is little detail of the involvement of UK-based students, Newton said that students in Britain were unlikely to be any different from their peers in the US and elsewhere, and warned that the UK “risks becoming a country where essay mills find it easy to do business”.

“There are a number of things the government could do to make contract cheating more difficult. The legal steps would probably include a new law – it’s not difficult, other countries such as New Zealand have done it and others like Ireland and Australia are thinking about it,” Newton said.

Staff at British universities regularly report essay-writing services openly advertising for both clients and writers on campus, while numerous websites offer students bespoke “study notes” or “essay aids” for a fee that runs into thousands of pounds depending on the length and deadline.

Essay mills also trawl social media, with automated accounts contacting students who post about essay deadlines and work panic.

Newton is one of a number of British academics who have warned of the dangers of “essay mills,” where students are able to order essays, dissertations or even doctoral theses with as little as eight or 12 hours’ notice. More than 2,000 people have signed a petition to parliament calling for a ban.

The study, published in the journal Frontiers in Education, analysed 71 survey samples from 65 studies from as far back as 1978, covering 54,000 participants who took part in questionnaires asking if they had ever paid someone to undertake their work.

Across the sample, contract cheating was self-reported by a long-run average of 3.5% of students but that rate was found to increase significantly over time. In studies from 2014 onwards, the percentage admitting to paying for work rose to nearly 16%, while cheating in general also appeared to be on the rise.

“There is an urgent need for a rigorous study to identify the extent of the problem in the UK. There’s a lot of circumstantial evidence to suggest the UK is as affected as everyone else,” Newton said, adding that surveys were if anything likely to underestimate the extent of the problem.

The government has recently acknowledged the issue. In a written answer to the Gower MP Tonia Antoniazzi in July, the higher education minister Sam Gyimah said: “We are currently focusing on non-legislative options, but remain open to the future need for legislation, and will investigate all options available.”

Newton and his colleagues have proposed a new offence, “to provide or advertise cheating services”, including writing or arranging an essay or other work without the approval of the higher education institution requiring the work.