The government is "absolutely looking at" lifting the cap on the number of places to study medicine, Health Secretary Matt Hancock has said.
The number of students studying to be doctors is regulated because of the cost and for NHS workforce planning.
But after this week's changes to A-level results, universities fear there will not be enough places for all the students with the grades to get in.
The body representing universities has called for the cap to be lifted.
The number of places to study medicine is the latest issue thrown up by the government's U-turn on Monday to change how exam grades are awarded, following a backlash.
The decision to give A-level and GCSE students the grades estimated by their teachers, rather than by an algorithm, means thousands of A-level students may now have the grades to trade up to their first-choice university offers.
Although the cap on overall student numbers has been raised, places at medical schools remain limited because the costs of training doctors far exceeds the fees paid by undergraduates.
In a letter to Education Secretary Gavin Williamson, seen by the BBC, Universities UK sought "urgent assurances" that he was speaking to the Department for Health about increasing the medical student cap.
"The role of universities in training the medical workforce is essential for all regions and nations of the UK, as clearly shown by our members' response to the Covid-19 pandemic," the letter said.
It also called more widely for "significant financial support" from the government as students are expected to change courses after being awarded higher grades.
The body, which represents 137 institutions across the UK, said that while the change to the grading method was the right decision, it would lead to grade inflation meaning universities with lower entry requirements would face a drop in course take-up and as a result require financial help.
The letter also asked for clarity on how increased student numbers could be managed alongside social distancing measures and guidance on how to handle a higher number of candidates with the required grades than available places.
Working 'immediately' on issue
Asked whether he would consider lifting the cap on medical students, Mr Hancock told BBC Breakfast: "We are looking at that.
"Thankfully we've got an expansion in the number of medical places this year, the biggest number of medical places ever, because we're hiring into the NHS, we're growing the NHS and we want to make sure the NHS has the doctors it needs in the future," he added.
"But I am absolutely looking at this issue, yes."
He later told BBC Radio 4's Today programme: "But of course there's now a huge number of pupils who have the grades, and so we're working very much immediately on how we can go further than we already are."
There have been planned increases in the number of medical school places available at English universities in recent years.
Prof Jenny Higham, principal of medical school St George's, University of London, told the BBC's Newsnight: "Medicine is both a very practical discipline and also requires a great deal of clinical and practical experience and hence clinical placement capacity also needs to be increased."
The pandemic has meant the current students have been unable to carry out their clinical studies meaning there is a backlog in places, she said.
Prof Higham added it was a high cost subject with courses funded by supplementary payments from the government as well as tuition fees, and the need to pay for clinical placements.
Conservative MP Sir John Redwood told Newsnight any changes also needed to be fair to the class of 2021 as well as "make up to the class of 2020", with next year's cohort needing to be assured of places if they got the necessary grades.
On Tuesday, universities minister Michelle Donelan said she wanted to ensure any students who had accepted a "different course" than planned, as a result of being downgraded last week, should be able to "change their mind and to reverse that decision".
She said No 10 was working with universities to help "boost the capacity available" in order to "minimise the amount of students that will be looking to defer."
Ministers in England, Northern Ireland and Wales all decided on Monday - four days after A-level results were issued - to revert to teacher assessed grades rather than the algorithm. Scotland reverted to teacher assessed grades on 4 August after facing a similar backlash.
The move prompted a scramble for university places as students tried to reclaim places at universities which they had last week been rejected from.
However, the top universities warned that students who now have higher grades could still be asked to defer if there is no space left on their chosen course.
Conversely, the Institute of Fiscal Studies is warning that lower-ranked universities may lose a substantial share of their intake, as candidates seek places on more demanding course. This could be "financially crippling", it says.
The chaos and uncertainty has led to calls from school and college leaders for an urgent review.
The education secretary apologised for the distress caused by the U-turn.