Some universities may be pushed to the brink of insolvency after the most cut-throat A-level student recruitment round vice-chancellors can remember, experts are warning.

The removal of the cap on the number of students universities can recruit, combined with a demographic fall in the number of 18-year-olds, has created a fierce new market in higher education. Prestigious universities are sucking up students who might previously have chosen mid-ranking institutions. The knock-on effect is leaving some universities without enough students – and their £9,250 fees.

Last Thursday, a week after results day, 352 higher education providers were still fighting for students in clearing – including 16 members of the elite Russell Group. And vice-chancellors say universities at all levels have been dropping grades to woo candidates.

Some report a frenzy of “mystery shopping”, especially in the first two hours of A-level results day, with university staff posing as parents or students on the phone to work out what competitors were really offering. As one vice-chancellor explains: “You then adjust your own offers accordingly. If a rival university sucks up 50 students by making lower offers you’ve lost those students. So there is a race to the bottom.”

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Nick Hillman, the director of the Higher Education Policy Institute thinktank, says: “We are closer to a bankruptcy scenario for a university than at any time in living memory.”

The vice-chancellor of a modern civic university, who asked not to be named, agrees: “We are heading for a car crash. I would say there are five or six universities who will run out of cash in two years’ time.” This is because “competition has been absolutely cut-throat. There are institutions at the bottom who can’t recruit enough students, so they drop their grades and let in students who can’t cope with the course and will drop out after one or two years. It’s just a slow death.”

Matt Robb, managing partner at the strategy consultancy EY-Parthenon, says struggling universities should act fast to sell land or buildings and shut courses with few takers. “Universities will go under if they choose not to act because of a misguided sense that the government will save them. It won’t.”

The government’s new Office for Students, unlike the old funding council, has no budget to bail out institutions.

The admissions service, Ucas, will not release data on numbers of students accepted at individual institutions for the new academic year until early 2019, and universities are all putting on a positive front during clearing. But figures released in January revealed that last year London Metropolitan University accepted 33% fewer students than in 2012. The university said this was a planned decline designed to manage its deficit. Over the same five-year period the University of East London and Southampton Solent University were each down 27% on accepted students; Cumbria University was down 24%, Kingston University 23% and the universities of Huddersfield and Sunderland were down 15%.

The pressure isn’t only felt at the bottom end of the sector. Universities of all types agree that there has been unprecedented behind-the-scenes dealing this year on the grades they will accept.

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Prof Alec Cameron, vice-chancellor of the mid-ranking Aston University, in Birmingham, says: “At the top end of the market we are seeing selective universities accommodating students who have missed their grades. And a lot of the low-tariff institutions are not publishing any grade requirements, so I’d say they are taking students with very low grades.”

Cameron says Aston, which officially takes students with an average of BBC, has this year been careful not to accept those with fewer than three Cs. “Like all universities we have been scrambling to enrol students through clearing. But we are trying to use judgment about whether they will succeed in the course. It’s to our long-term detriment if we encourage the wrong students, as they might drop out.”

The head of one leading research university says: “There is now a mammoth gap between where institutions say they are in grade terms and what they really accept. The scramble to get a student is profound.”

He adds: “You can be ranked 19 in the country and still face a crisis because you are losing out to more popular competitors. There is a trade-off between the numbers you need per subject and what grade drop you’re prepared to take.”

Hillman says the consequences can be serious. “Dropping the grades you accept matters if it affects your drop-out rate and, eventually, your league table position.”

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Richard Harvey, academic director of admissions at the University of East Anglia, says tensions are high because most universities have growth plans. “They shouldn’t, of course, because the numbers of students are actually contracting.”

Sarah Stevens, head of policy at the Russell Group, says: “The average tariff score for new students entering our universities has remained broadly steady over recent years. In fact, students entering Russell Group universities are now slightly better qualified than they were 10 years ago.”

De Montfort University’s vice-chancellor, Prof Dominic Shellard, makes no secret of the fact that clearing is big business. “You’ve got to get the right number of appropriate calibre students through your doors in August,” he says. “Everything else stems from that.”

This year the university fielded 7,200 phone calls in the first three days of clearing. Shellard, a football fan, persuaded three stars of the local club, Leicester City, to answer the phones on results day. Students could also talk through their options on WhatsApp, Snapchat, Instagram, Facebook and Twitter, and in the first few days De Montfort made 50 official offers via WhatsApp.

•This article was amended on 28 August 2018. An earlier version said Leicester City players were paid by De Montfort University to answer phones. This was incorrect. The players were involved as part of an ongoing partnership between the university and the club.