image copyrightUniversity of Exeterimage captionStudents are being asked to defer their place at the university's medical school.
Students wanting to study medicine at the University of Exeter are being offered free accommodation and £10,000 cash if they are prepared to delay their course for a year.
A record number of students have applied to study medicine this autumn, a rise of more than 20% on last year.
The number of places for medicine in England is capped by the government.
If students delay until 2022, that could reduce the number of places available for those applying next year.
The University of Exeter has written to students who have accepted an offer to study medicine starting in 2021 asking if they will delay to 2022.
In return it would guarantee their place next year, provide free accommodation for their first year and a cash bursary of £10,000 "to spend on preparing yourself" at the end of October 2021.
The accommodation in the university's Rowancroft accommodation building would normally cost £6,574 for an en-suite room or £7,611 for a studio flat.
The letter to students says the university understands this would mean "big changes" to their plans but their place next year would be secure, provided they get the grades specified in their offer.
Professor Mark Goodwin, Exeter's deputy vice chancellor, said it had seen a significant increase in students who had prioritised the university as their first choice for medicine.
"This is unprecedented for us, something has happened this year to make a higher proportion choose us. More students are holding us as their firm choice this year"
As the numbers admitted to the course are regulated by the government, the university is asking applicants holding a firm offer to decide by 30 July if they will defer.
"We want to deliver a really high quality student experience, and deliver those safe and secure NHS placements so we can train the number of doctors the government asks us to train."
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image copyrightUniversity of Exeterimage captionPlaces to study medicine are limited by the government
Places to study to be a doctor are limited by the government, partly because of the large subsidy needed from public funding to meet the high cost of around £180,000 for a medical degree.
Every medical student also has to undertake clinical placements in the NHS in the last three years of the degree.
So universities are given an allocation of places which they cannot exceed.
It is always competitive to get a place in medical school, with around three applicants chasing each place on average.
Dr Katie Petty-Saphon from the Medical Schools Council says the increase in applications this year has made it harder for universities to judge the right number of offers.
"In the past the very best applicants might receive four offers which would mean they would reject – and thus free up – places at three medical schools.
"This did not happen this year and so the 'conversion rate' of offers to firmly accepted places has changed, meaning that some medical schools have more acceptances than they were anticipating."
She added there are the same number of places in England this year as usual, around 7,500.
However, universities are also accommodating students who had to defer after the chaos of last year's A-level grading left more than usual with the grades they needed.
"The government has funded 450 additional places for applicants who were required to defer last year – and so such candidates are not taking up places destined for 2021 applicants" said Dr Petty-Saphon.
It is not clear if extra money would be available from the government for additional places next year, which could mean students applying to Exeter competing for fewer places.
While Exeter has written to students holding offers, other medical schools will be grappling with similar issues, albeit on a smaller scale.